














s, « 










































o> ,-tf. 




^ •<! 









x° Xi 



v /' ^ 



..V 



c, «/> 



A X 



4 









<- * o i A * \ V 












, % 



\^> 









*% 






** ,.\ 












N ^ 









/ > 



\* , 



%.# 















* 






/' 















V* 






























r> , 



-y 



++ J 



^ 



> 












%<p 







?% 



H, 






L^ <?, 







5s /■ '/■'/ 



-> 



*> \> s 



%& 













THE 



THEORY 




REA S~0 N : I N G. 



BY 



SAMUEL 



BAILEY. 



LONDON: 
LONGMAN, BROWN, GREEN, AND LONGMANS. 

1851. 



<3 



Q,^ 



<5>v 



THE UMAET 

or c one* *— I 

WASHlWOTOir 



. 



fc/ 



PREFACE. 



The following Treatise aims at giving a connected 
and consistent view of the subject which it under- 
takes to explain, and of the relation in which the 
several parts of it stand to each other. Perhaps 
, will not be considered as departing from the 
proper self-restraint which leaves the question 
of originality to be decided by others, if the 
Author ventures to say that this connected view 
differs as a whole, and of course in some of its 
details, from any theory hitherto promulgated. 
Saying this is, indeed, putting forth no claim 
except to the attention of the reader, inasmuch 
as there can be no merit in any difference from 
former writers, unless that difference is founded 
in truth. 

The Author designed at first to make the Treatise 
almost wholly expository ; but the number of un- 
settled questions on which he had to touch, forced 



VI PREFACE. 

him more extensively into criticism and controversy 
than he had originally contemplated entering. In 
such a work it was especially impossible not to 
advert to the scholastic logic ; and as his theory 
is at variance with some of its fundamental prin- 
ciples, he has had occasion to comment upon it at 
considerable length. 

If, in doing this, he has, on the one hand, been 
obliged to differ very widely on certain points 
from several of the ablest logical writers of the 
day, he has, on the other, found himself in ac- 
cordance on many of the same points with some 
of the most eminent philosophers of the past and 
present ages. 



February 22. 1851. 



CONTENTS. 



Page 

Chapter I. The Intellectual Operations which pass 

under the name of Reasoning - - 1 

Chapter II. Contingent Reasoning - - 7 

Section 1. The Nature and Cogency of Contingent 

Reasoning - - - 7 

Section 2. Contingent Reasoning distinguished from 
Knowing, on the one hand, and Con- 
jecturing, on the other - -25 

Chapter III. Demonstrative Reasoning - - - 33 

Chapter IV. Contingent under the Form of Demonstrative 

Reasoning - - - - 45 

Chapter V. The Intermixture of Contingent and De- 
monstrative Reasoning - - -56 

Chapter VI. Principles of Reasoning or Maxims, and 

especially the Dictum de omni et nullo - 60 

Chapter VII. Forms of Reasoning, and especially the 

Syllogism - - - - 77 

Chapter VIII. Primary or Original Premises - - 94 

Chapter IX. The Relation between Reasoning and 

Language - - - - 99 

Chapter X. The Relation of Observation, Experiment, 
and Induction, to Reasoning and to 
each other - - - - 113 



Vlll 



CONTENTS. 



Page 
Chapter XL Rules for guiding the Operations of 
Reasoning, and especially the Rules of 
the Scholastic Logic - - -122 

Section 1. Rules in Contingent Reasoning - - 123 

Section 2. Rules in Demonstrative Reasoning, and 

especially in Syllogistic Reasoning - 127 

Section 3. Subject continued : Mode of using the 

Syllogistic Form - - - 130 

Section 4. Subject continued : Rules of the Scholastic 

Logic- - - - - 133 

Section 5. Subject continued : Rules of the Scholastic 

Logic- - - - 146 

Section 6. Subject continued: Effects of the Scho- 
lastic System as a Discipline of the 
Mind 159 

Chapter XII. The Sources of Erroneous Conclusions - 165 



APPENDIX. 

Article I. An Analysis of some Trains of Reasoning- 185 
Section 1. Analysis of a Demonstration in Euclid - 185 
Section 2. Analysis of a Passage in Burke - - 188 

Article II. Some Suggestions for the Examination of 

Argumentative Composition - - 197 

Article III. The preceding Suggestions in part exem- 
plified by an Examination of Berkeley's 
Argument to prove the impossibility of 
seeing Distance - 200 



THE 



THEORY OF REASONING, 



CHAPTER I. 



THE INTELLECTUAL OPERATIONS WHICH PASS UNDER 
THE NAME OF REASONING. 

In scrutinizing our own minds, several different 
operations are easily distinguishable, and have ac- 
cordingly received particular appellations. When 
present objects are discerned through the senses^ 
the act is usually named perception ; when objects 
formerly perceived by us, or facts formerly known 
to us, are recalled, the mental event is denominated 
recollection, or mere conception ; when objects or 
facts occur to the mind in a different order or com- 
bination from that in which they were actually 
perceived, there is something more than conception, 
and it has been termed imagination ; lastly, when 
facts perceived determine the mind to the belief of 
facts which it does not perceive, although here also 

B 



Z THE THEORY OF REASONING. 

conception is implied, the operation is evidently as 
distinct from the former three operations as they 
are from each other. 

This intellectual process may be illustrated by a 
few familiar instances. 

I am walking, I will suppose, on the sea-shore, 
and perceiving a quantity of sea- weed lying on the 
beach, while the water is at the moment a quarter 
of a mile from it, I conclude that the tide has 
ebbed, and left the weed where I perceive it lying. 
I notice the print of a small foot on the sand, 
and I feel pretty sure that it was made by a child. 
I look upon the multitude of gay people walking 
along the beach, and I am struck with the thought 
that sooner or later, and, at the latest, in no very 
long period, they must all die. 

I observe the sun to be exactly on the meridian, 
and I calculate that at a place where a friend of 
mine resides, 15 degrees in longitude to the west of 
my position, it is just eleven o'clock. 

In these several cases my mind is determined by 
the sight of present phenomena, conjoined with 
knowledge previously acquired, to believe some- 
thing which I do not actually perceive through the 
organs of sense ; something past, something future, 
or something distant ; or, in other words, to be- 
lieve that some event has happened, will happen, or 
is happening, although beyond the sphere of my 
observation. 

But the actual presence of any facts to the senses 



THE THEORY OF REASONING. 6 

is not essential to the operation in question. I 
may recollect or be told of a fact, and thus knowing 
it from recollection or testimony, I may form the 
same inferences from it as if I perceived it. 

This determination of the mind to the belief of 
something beyond its actual perception or know- 
ledge, is obviously what is termed reasoning. 

There is, however, another mental operation to 
be noted, which consists, not in our being led to 
believe, or in our inferring from what we perceive 
and know, something else, neither perceived nor 
known ; but in our being led to discern some fact, 
not directly manifest, through the medium of some 
other fact or facts in which it is implied. 

Suppose somebody to assert that the opposite 
angles made by the intersection of two right lines 
are equal. This, at the first glance, appears likely 
enough to be true ; but it is not intuitively per- 
ceived, it is not immediately a 
manifest. When, however, he 
proceeds to point out that the 
angles abd and abc are toge- 
ther equal to two right angles, 
and that the angles abd and 
d b e are also together equal to 
two right angles, we discern D & 

that these two pairs of angles are equal to each 
other ; and when he further points out the circum- 
stance of the angle abd being common to the two 
equal pairs, we at once discern that the other angle 

B 2 




4 THE THEORY OF REASONING. 

A b c of the first pair is equal to the other angle 
D B e of the second pair. 

Here we do not infer the existence or the hap- 
pening of something past, or future, or absent ; but 
we are led to discern something not directly ob- 
vious, by an arrangement of propositions expressive 
of facts, each of which implies its successor. 

To describe it more particularly : 

The complex fact, or combination of facts, ex- 
pressed in the proposition, " the two pairs of angles 
are respectively equal to two right angles," implies 
(or leads the mind to discern) that they are mu- 
tually equal ; and the fact that the pairs, thus 
proved to be equal, have one angle in common, 
implies (or leads the mind to discern) that the 
remaining angle in the one is equal to the remain- 
ing angle in the other. Thus, if we regard the 
facts, there is self-evident involution or implication ; 
and if we regard the mind of the reasoner, there is 
intuitive discernment at every step of the process. 
/ The operation just described is termed reason- 
ing equally with the other ; but there is evidently 
an important difference between them. To be de- 
termined by facts to the belief of an unobserved 
event or object, past, present, or future, and to 
discern when two facts are presented to the mind, 
that one is implied in the other, are intellectual 
acts or operations plainly distinct. If there were 
no other circumstance by which to discriminate 
them, they would be broadly distinguished by this, 



THE THEORY OF REASONING. 5 

that in the latter species of reasoning, every step 
being discerned to be necessarily true, the denial of 
the conclusion involves a contradiction, while in 
the former species it does not. The conviction in 
the one case, and the discernment in the other, 
have, nevertheless, this in common, that the fact 
expressed in the conclusion is not in either case 
evident of itself, but is arrived at through the 
medium of some other fact or facts. 

Of these two species of reasoning, while the 
second has been uniformly termed demonstrative, 
the first has sometimes been called moral, and 
sometimes probable reasoning ; but on account of 
the ambiguity of these appellations, as will be ex- 
plained in the next chapter, I shall venture to 
speak of it under the designation of contingent 
reasoning. Although objections may doubtless be 
brought against the epithet contingent, so applied, 
it appears to me, on mature consideration, to be 
less exceptionable and more convenient than any 
other. 

The facts which determine the mind to the belief, 
or lead it to the discernment of other facts not im- 
mediately manifest, are usually spoken of under 
the designation of evidence or proofs ; and when 
expressed in propositions preceding a conclusion, 
under that of premises. 

To reason, is to go through proofs or evidence 
for or against any alleged fact. Frequently the 
fact alleged or expressed in the conclusion is placed 

B 3 



6 THE THEORY OF REASONING. 

before the mind first, and the proof is adduced to 
substantiate it ; but it also frequently happens, in 
the course of reflection, that a fact, or combination 
of facts, leads the mind to the belief or to the dis- 
cernment of a fact before unknown, which is then 
seen in its logical place as the conclusion. 



CHAP. II. 



CONTINGENT REASONING. 



The preceding chapter having shown that there 
are two distinct mental processes which pass under 
the name of reasoning, I purpose next to inquire 
more closely into the nature of the first of these 
processes, the principles on which it proceeds, and 
the foundation of its cogency. 



Section I. 
The Nature and Cogency of Contingent Reasoning. 

Let us examine any simple instance of the first 
species of reasoning. The one already cited, re- 
specting the sea-weed found on the beach, may 
serve the purpose. What takes place on such an 
occasion may be described as follows : — 

Having previously observed the tide, in ebbing, 
leave the sea-weed high upon the beach, as I see it 
at the present time, the recollection of this fact 

B 4 



8 THE THEORY OF REASONING. 

causes me to believe that the phenomenon before 
me has had the same origin. 

Here the mind is obviously determined by pre- 
sent appearances, conjoined with what has been 
previously observed, to believe in a past event 
which has not actually fallen under observation. 

In the inference, also given in the preceding 
chapter, " that the gay people walking on the beach 
will, sooner or later, all die," the mind is likewise 
determined, by previous observation or knowledge, 
to the belief of events concerning the objects before 
it, which, from the nature of the case (being yet to 
happen), cannot have been observed ; but there is 
this difference: — in the first example, a past event 
is inferred from other past facts ; in the second, 
future events are inferred from past events. 

It is scarcely necessary to point out again, that, 
in another illustration before adduced, a contempo- 
raneous event or fact beyond the sphere of the 
reasoner's observation is inferred from what is 
taking place before his eyes, with the assistance of 
previous knowledge. 

In all these examples alike the mind is deter- 
mined to the belief of an event or fact not witnessed 
or known, or, in other words, it infers an event or 
fact which it has not the means of immediately 
observing. 

For such inferences one condition is always ne- 
cessary. The reasoner must have been acquainted. 



CONTINGENT SEASONING. V 

with a similar case or similar cases. We are deter- 
mined to the belief of an unobserved fact by having 
observed or known a similar fact to have taken 
place in similar circumstances. It is this resem- 
blance in the cases which leads us to infer that 
unobserved events have happened, are happening, 
or will happen. 

Tn simple cases, where the complete resemblance 
of objects or events is at once discerned, a single 
previous instance frequently suffices for an infe- 
rence ; but in complicated cases, where there is 
similitude with some degree of diversity, a collection 
and comparison of various instances is necessary to 
show that the diversity does not affect the essential 
circumstances on which the event depends, and that 
the instance about which we are reasoning does not 
differ from the others, in which the event has been 
observed, more than they differ from each other. 

Thus, to revert to the examples already adduced, 
I may have observed the action of the tide on the 
sea-weed only once, yet, when I see the weed lying 
as before described, I instantly conclude that it has 
been left by the retreating waves. 

In the same way, when I draw the conclusion 
that a child has passed over the sand, from the 
marks imprinted upon it, all that is necessary for 
the inference is the previous observation of a single 
fact of a similar kind. 

On the other hand, when I conclude that my 



10 THE THEORY OF REASONING. 

fellow-creatures around me will sooner or later die, 
my inference is from a large number of facts known 
to me in various ways, some gathered from per- 
sonal observation, some collected from the history 
of the race, and the whole expressible in the pro- 
position that all men in every climate, how different 
soever in constitution, character and habits, after 
living a certain limited period, have died. 

It is obvious, that whether we can draw an in- 
ference from a single fact, or whether it is needful 
to have a collection of facts, depends altogether on 
what is requisite for establishing a similarity in the 
influential circumstances of each case, and does not 
affect the character of the reasoning, which is still 
inferring, or being determined by what we are 
cognisant of, to believe something beyond what is 
observed or known. 

In the examples of reasoning already cited, the 
conclusions, it is to be remarked, are all relating to 
definite objects, and may be called particular in- 
ferences ; but there is another large and important 
class of conclusions from analogous premises, which 
are general or universal. 

The same facts which determine us to believe 
that a single individual, or that the crowd we see 
on the beach, will die, determine us to believe that 
all human beings will die ; or, to express it in still 
more general terms, that all men are mortal. That 
these inferences which are usually termed general 



CONTINGENT REASONING. 11 

laws, are precisely of the same nature, and rest on 
the same evidence as particular inferences, is ma- 
nifest. They both alike predicate the unknown 
from the known, and differ only in the extensive- 
ness of their subject. 

From what may be conveniently termed the col- 
lective fact, that men have hitherto been fallible as 
far as observation has extended, I may deduce the 
particular conclusion that an unknown and untried 
individual named Peter is fallible, and I may 
equally deduce the universal conclusion that all 
men are fallible. 

In the latter case, it is instructive to mark the 
superior range of the inference from the same pre- 
mises. The proposition that all men are fallible, 
not only embodies actual knowledge, but as- 
serts an intellectual imperfection in human beings 
whose mental condition and endowments have 
never been ascertained. It affirms, not only that 
in all known or observed instances, men have been 
found fallible, but that all human beings who have 
existed in time past, unknown and unobserved, 
have laboured under the same defect ; that all men 
now living, known or unknown, are subject to it ; 
and that all who shall hereafter exist will also be 
similarly constituted. 

In illustration of what has been said, let us place, 
side by side, the universal law, and the particular 
inference from the collective fact. 



12 THE THEORY OF REASONING. 



COLLECTIVE FACT. 



All men, as far as observation has extended, have been found 

fallible. 



Universal Law. Particular Inference. 

Therefore all men are fallible. Therefore the man Peter is 

[i. e., men of past times be- fallible, 

yond the reach of observa- or, 

tion, as well as those ob- The next generation of men 

served, were fallible ; men of will be fallible, 

the present time, whether or, 

observed or unobserved, are Socrates, who lived more than 

fallible, and all future men two thousand years ago, was 

will be fallible.] fallible. 

It is obvious that both these conclusions, both 
the universal law and the particular inference, are 
deduced from the same fact or collection of facts : 
they are, if I may so express it, abreast, or co- 
ordinate ; one is not, or needs not be logically sub- 
sequent to the other ; or, to vary the language, 
both are probable inferences, for which the real 
evidence is the same. The mental process too is 
alike ; it does not consist in the mind's discerning 
one thing to be implied in another, but in its being 
determined by known facts to believe unknown 
ones. 

Much error and confusion, it appears to me, has 
arisen from not distinguishing between the collec- 
tive fact, which is simply a summary of the 
evidence, and the general or universal law inferred, 



CONTINGENT REASONING. 13 

which goes beyond the evidence. I cannot help 
thinking, that Dr. Thomas Brown, with all his 
acuteness, has either not discerned the distinction, 
or not always kept it clearly in view, as, for ex- 
ample, in the following passage, which, even if I am 
not correct in my interpretation of it, will assist 
me to explain the point under consideration. 

" If by the term general laze be meant," he says, 
" the agreement in some common circumstances of 
a number of events observed, there can be no 
question that we proceed safely in framing it, and 
that what we have already found in a number of 
events, must be applicable to that number of events. 11 
— " But the only particulars to which in this case 
we can with perfect confidence apply a general law, 
are the very particulars that have been before ob- 
served by us." # 

This might be taken as a good description of that 
which is necessary to constitute what I have termed 
the collective fact, but it would be an incorrect 
description of what is usually meant by a general 
law, unless we construe the phrase the very par- 
ticulars to denote, not the identical facts, but ex- 
actly similar facts. 

It would, however, be taking an imperfect view 
of the subject to suppose that we reason only from 
such collective facts as may be denominated uni- 
form. 

* Lectures, vol. i. p. 176. 



14 THE THEOEY OF REASONING. 

Besides the cases I have already noticed, where 
the similarity of the influential circumstances is 
maintained amidst a certain diversity in other 
respects, there are innumerable cases of a compli- 
cated, and not altogether definite character, in 
which a certain result has not always happened, but 
has taken place in more instances than it has failed 
to take place, and others in which a result has 
failed oftener than it has happened. When a new 
instance of the first kind presents itself, we infer 
the probability that the event will happen to be 
greater than the probability of its not happening ; 
when an instance of the second kind is before us, 
we infer the probability of its happening to be less 
than the probability of the contrary ; which proba- 
bility, it is almost needless to observe, admits of 
degrees, according to the varying circumstances of 
each instance. 

The nature of the reasoning in these cases is the 
same as in those where the facts are uniform, and 
it is only in the degree of probability which is re- 
cognized that the conclusions differ. It is obvious 
that the want of uniformity in the result is owing 
to a want of uniformity in the presence of the 
influential circumstances. Although the subjects 
of the proposition which expresses the fact are 
comprised in a general term or description, yet 
they are alike only in certain respects, and some of 
them differ in points on which the result depends. 
For example, it is a general observation, that man- 



CONTINGENT SEASONING. 15 

kind follow the religion of their immediate ances- 
tors ; but this, although generally, is not invariably 
the case. Men are compound beings of varying 
qualities, and a few in almost every country, in 
consequence of peculiar circumstances, or intel- 
lectual idiosyncrasies, are found to depart from the 
hereditary creed : whence, if you happen to meet 
with a native of Turkey or Eussia, you cannot 
infer, from his country alone, that the former holds 
the Mahometan faith, nor the latter that of the 
Greek Church. If your knowledge of this single 
circumstance is your only guide, your correct 
inference will be that he is very probably of the 
same religion as the great majority of his fellow- 
countrymen. 

My explanation of the nature of contingent rea- 
soning would be incomplete, without adverting to 
one point connected with it, which has not always 
been seen in its true light. Every act of reasoning 
(as I shall have occasion to show at greater length 
hereafter) proceeds upon, or exemplifies, some ge- 
neral principle ; or, in other words, from every act 
of reasoning some general principle may be drawn 
or educed *, which may for shortness be called the 
principle of the reasoning. 

* The term " deduce" being already appropriated to the 
operation of inferring conclusions from premises, it may con- 
tribute to precision, where precision is much wanted, to adopt 
the term " educe' to denote the process of forming or drawing 
out the general principle which, according to common phraseo- 



16 THE THEOKY OF REASONING. 

We have, therefore, to inquire, what is the prin- 
ciple of the species of reasoning now under con- 
sideration, and we shall find it to be as follows: — 
What has been observed to take place in a similar 
case, or in all similar cases, has taken place, is 
taking place, or will take place in the case before 
us, where actual observation is precluded ; or, more 
briefly, without reference to time, similar events or 
phenomena take place in similar cases. 

This will appear sufficiently manifest if we dwell 
for a moment on the conclusion before men- 
tioned, that all the persons walking on the beach 
must sooner or later die. The reason, as we 
have already seen, which determines the mind to 
this conclusion is, that all human beings formerly 
living have died before attaining a certain age. 
Briefly expressed, the reasoning is — 

All human beings formerly living have died 

before attaining a certain age : 
Therefore, these human beings will die before 
attaining that age. 

And the general principle which is exemplified 
here is, that similar events will take place in similar 
cases. 

A principle of reasoning may hence be regarded 
as a generalised statement, or description of what 
our inferences consist in ; or of what we do when 
we draw them. It may be remarked, too, that a 

logy, is involved in an argument, or on which an argument 
proceeds. 



CONTINGENT REASONING. 17 

general principle of this kind includes subordinate 
or less general principles, as classes include genera, 
and genera include species. We might, for instance, 
from the last example educe the principle, " What 
has happened to all human beings formerly living, 
will happen to all now living." Moreover, as the 
chief cases of similarity are those of causation, the 
two main subordinate principles in contingent rea- 
soning may be stated briefly to be, " Like causes pro- 
duce like effects, and like effects proceed from like 
causes." 

The next important point for our investigation 
is, how is the cogency of this kind of reasoning, 
which is confessedly not demonstrative, to be 
proved ? To which I answer, that the cogency of 
no direct and simple process of reasoning can be the 
subject of proof. The only question is, does the 
reasoning, when clearly expressed, produce convic- 
tion ? or, in other words, do the facts, when pre- 
sented clearly to the mind, determine it to believe 
that which is expressed in what is called the con- 
clusion ? If they do, we have reached an ultimate 
fact, or law, or principle of our mental constitution 
beyond which it is impossible to go. It may be laid 
down as a general law or expression of this fact, 
that the human mind is determined to the belief of 
similar events in similar cases. The argument 
already cited, that the human beings whom we are 
now looking upon will die before reaching a certain 
age, because all other human beings, or rather all 

c ■.■■/. 



18 THE THEORY OF REASONING. 

human beings formerly living, as far as observation 
has extended, have so died, produces conviction at 
once, and nothing can enhance or diminish its 
power. It is deserving of especial remark that 
drawing out the general principle implied in the 
argument or educible from it is of no avail in 
strengthening its force, although the contrary has 
been frequently assumed, and even expressly as- 
serted. The cogency of the reasoning in the par- 
ticular example is quite as manifest as that of the 
principle on which, according to the common 
phrase, it proceeds, or which is involved in it. The 
maxim that what has been observed invariably to 
happen in certain cases, has happened and will 
happen in all precisely similar cases, is only a 
generalisation of the reasoning which is exhibited 
in particular instances, and has no proving power 
of its own. 

It is this step taken by the mind, or rather this 
determination of the mind by known facts to believe 
unknown ones, which gave rise to Hume's cele- 
brated speculations in his chapter entitled " Scep- 
tical Doubts." He was not satisfied to receive it as 
an ultimate principle beyond which we could not 
go, but wanted an explanation of its origin in some 
other principle. After remarking that from the 
fact of having been formerly nourished by eating 
bread, it does not necessarily follow that we shall be 
nourished by eating other bread, he proceeds, u At 
least it must be acknowledged that there is here a 
consequence drawn by the mind ; that there is a 



CONTINGENT REASONING. 19 

certain step taken, a process of thought and an in- 
ference which wants to be explained. These two 
propositions are far from being the same, 'I have 
found that such an object has always been attended 
with such an effect] and i I foresee that other objects 
which are in appearance similar will be attended with 
similar effects.' I shall allow, if you please, that 
the one proposition may justly be inferred from the 
other : I know, in fact, that it always is inferred. 
But if you insist that the inference is made by a 
chain of reasoning, I desire you to produce that 
reasoning. The connexion between these proposi- 
tions is not intuitive. There is required a medium 
which may enable the mind to draw such an in- 
ference, if indeed it be drawn by reasoning and 
argument. What that medium is, I must confess 
passes my comprehension ; and it is incumbent on 
those to produce it who assert that it really exists, 
and is the original of all our conclusions concerning 
matters of fact." * 

In this passage there are three points to be 
especially remarked. Hume affirms, 1st., that such 
inferences as he describes are always drawn, and 
justly drawn: 2. that the connexion between the 
inference and the proposition from which it is 
drawn is not intuitively perceived: 3. that the in- 
ference wants explanation ; and while he himself 
asserts that a medium or chain of reasoning is 
required to enable us to draw the inference, he 

* Sceptical Doubts, Part II. 
c 2 



20 THE THEORY OF REASONING. 

confesses that what that medium is passes his com- 
prehension, and he challenges others to produce it. 
Now, in the first and second of these assertions he 
is perfectly correct, and his view of the subject 
corresponds with what has been said in the previous 
part of the present chapter; but in the third he 
requires an explanation which is needless, and he 
challenges his imaginary adversaries to produce 
what is totally uncalled for, and cannot possibly be 
given. If, as he says, an inference is unavoidably 
and justly drawn, no medium or chain of reasoning 
is needed to enable us to draw it. Drawing an in- 
ference is reasoning, and between the inference and 
the fact from which it is drawn nothing can, in the 
nature of the case, be interposed. All that he says 
merely shows that there is a species of reasoning in 
which we unavoidably infer unknown? facte from 
known facts ; and that this is a different species of 
reasoning from that in which we intuitively discern 
one fact to be necessarily implied in another. 

Reid, Dugald Stewart, and Thomas Brown, do 
not follow Hume in his demand for a medium, but 
they unite with him in declaring that inferences 
of the kind in question are not drawn by reasoning. 

If we construe this declaration literally, it 
amounts in fact to saying that we do not reason by 
reasoning, which may be true, but it is at all 
events nugatory. "We cannot, certainly, be said 
with any propriety to do an act by the act itself 
but who would think of making the assertion ? 



CONTINGENT REASONING. 21 

There are two different propositions, relating 
to this point, which may easily be confounded, 
viz. : " these inferences are not drawn by reason- 
ing," and " drawing these inferences is not reason- 
ing." The former, as I have just explained, if 
taken literally, is a trifling and worthless assertion, 
which, perhaps, in fairness to these philosophers 
we ought not to attribute to them ; they probably 
meant that such inferences are not demonstrated, 
and that there is no absurdit}^ in supposing them 
to be false, the universal test of demonstrative 
arguments. 

With regard to the latter proposition, viz. 
that " drawing these inferences is not reasoning," 
we are precluded from assuming this to have been 
their meaning, for it would be inconsistent with 
their own practice, which is constantly to speak of 
the drawing of such inferences as reasoning. Hume 
in one place denominates it experimental reasoning. 
Dr. Eeid usually terms it probable reasoning, and 
one short passage selected from a number of 
others proves that by this phrase he intended to 
designate such inferences as are now in question. 
" In probable reasoning the connexion between 
the premises and the conclusion is not necessary, 
nor do we perceive it to be impossible that the 
first should be true while the last is false." * 

Mr. Stewart uses language equally or still more 

* Essays on the Powers of the Human Mind, Essay vii. 
chap. i. 

c 3 



22 THE TliEOKY OF REASONING. 

obviously in point, where he speaks of " the prin- 
ciple of my nature which leads me thus not only 
to reason from the past to the future, but to reason 
from one thing to another, which, in its external 
marks, bears a certain degree of resemblance to 
it." * 

The words of Dr. Brown in proof of a similar 
use of the term reasoning, need not be cited in 
form. The reader will find a passage in his Lec- 
tures perfectly explicit and appropriate, where he 
speaks of the " reasoning of infants." f 

It might be well, perhaps, if we had a generic 
name by which to distinguish .contingent from de- 
monstrative reasoning ; but since we are accus- 
tomed to employ the same expressions in regard 
to both, applying to them in common such terms 
as proofs, premises, consequences, inferences, conclu- 
sions, and making use, in both cases, of the same 
causal and illative conjunctions, because, inasmuch, 
then, therefore, consequently, the only feasible plan 
seems to be, to discriminate them as species of the 
same genus. It seems impossible, without altering 
the whole structure of language, to do otherwise. 

Another consideration in favour of this method 
is, that not only are contingent and demonstra- 
tive reasoning often intermingled, but there is 
much reasoning, as I shall hereafter explain, which 

* Philosophy of the Human Mind, vol. ii. p. 241. 
f Lectures on the Philosophy of the Human Mind, vol. ii. 
p. 526. 



CONTINGENT REASONING. 23 

partakes of the character of both ; which, while it 
is contingent in reality, is demonstrative in form. 

What is the most appropriate specific appella- 
tion that could be adopted for that reasoning 
which is not demonstrative, is a question of some 
nicety ; nor will I pertinaciously contend that I 
have made the best possible choice in selecting the 
term contingent. 

Some authors, as already stated, call this species 
of reasoning moral, and others probable, while a 
third class use the two epithets interchangeably. 
To the term moral there is the objection that it is 
already used in several acceptations ; and further, 
that the reasoning so designated frequently relates 
to purely physical or material subjects. To the 
term probable there is the objection that it is 
usually employed in the sense of likely, and is 
qualified by epithets expressive of degrees. Cases 
might easily be imagined in which these two senses 
would clash : e. g. it might happen that we should 
have to prove by probable reasoning that an event 
was exceedingly improbable. * 

* " The word probable" says Mr. Stewart, " does not imply 
[i. e. when philosophically used] any deficiency in the proof, 
but only marks the particular nature of that proof, as contra- 
distinguished from another species of evidence. It is op- 
posed, not to what is certain, but to what admits of being 
demonstrated after the manner of mathematicians. This differs 
widely from the meaning annexed to the same word in popular 
discourse ; according to which, whatever event is said to be 
probable is understood to be expected with some degree of 
doubt." — Elements, vol. ii. p. 252. 

c 4 



24 THE THEORY OF REASONING. 

Perhaps, one of the best designations is inductive, 
which was employed by Dr. Eeid in his earliest 
work, but which he appears to have subsequently 
laid aside. Since induction, however, as commonly 
understood, denotes a complex operation, viz. col- 
lecting and scrutinizing facts, preparatory to in- 
ferring a general law from them, and sometimes 
inferring the general law itself, the designation 
seems hardly appropriate in simple cases, where, as 
is often done in this species of reasoning, we infer 
one particular fact from another. 

The terms moral, probable, inductive, contin- 
gent, and demonstrative, direct the attention to 
the nature of the proofs or evidence before the 
mind, but we might select names which would 
point to the intellectual operations themselves. 

Hume * and other writers, in discussing the 
origin of the inferences we draw from the past to 
the future, from the known to the unknown, have 
ascribed them to instinct ; and philosophers gene- 
rally have referred our discernment of the steps in 
demonstrative deductions to intuition. 

Adopting this view and this phraseology, we 
might denominate the first species of reasoning 



* See several passages in his " Sceptical Doubts," and 
" Sceptical Solution of these Doubts." I will quote, however, 
a passage from his " Academical Philosophy " on account of 
its brevity, certainly not of its consistency. " Nothing leads 
us to this inference but custom, or a certain instinct of our 
nature." — Essays and Treatises, vol. ii. p. 161. 



CONTINGENT REASONING. 25 

instinctive, and the second, intuitive. We infer in- 
stinctively that the bread we are eating will nourish 
the body as other bread has done : we conclude in- 
tuitively that the lines A and b being respectively 
equal to c are equal to each other. 

On giving the subject, however, the best consi- 
deration in my power, I have preferred the terms 
contingent and demonstrative, without precluding 
myself from the occasional use of any others when 
no misunderstanding can arise. If the former is 
not absolutely the most appropriate (in regard to 
which there is fair scope for diversity of taste and 
judgment), it will at all events enable me to ex- 
plain my views with sufficient precision : respect- 
ing the latter, I am not aware that there ever has 
been any difference of opinion whatever. 



Section II. 

Contingent Reasoning distinguished from Knowing 
on the one hand and Conjecturing on the other. 

There is one objection which, I am aware, may 
be urged against the view now presented of the 
reasoning process in contingent matters, and it is 
this, that it would dignify nearly every intellectual 
act with the name of reasoning ; that it would, on 
the one hand, confound reasoning with positive 
knowing, and, on the other, with mere conjectur- 



26 THE THEORY OF REASONING. 

ing ; embracing many cases of instantaneous and 
habitual apprehension which it would seem puerile 
to term cases of inference, and many others which 
are bare guesses or whims of the imagination. 

The allegations here supposed might, however, 
be allowed, might even be true, without at all in- 
validating the representation of the reasoning pro- 
cess against which they are directed. It would be 
no impeachment of the doctrine of this treatise to 
admit, that although there is a broad distinction 
between the mental acts alleged to be confounded, 
when we consider very decided cases, yet in many 
instances it would be difficult to draw a line of 
demarcation on either side. The colours of the 
rainbow which are sufficiently contrasted when we 
regard the middle of each stripe, are so insensibly 
blended together that it is impossible to perceive 
where one ends and the other begins, yet no one 
on this account denies the existence of the seven 
prismatic colours or the propriety of giving them 
separate names : and, in the same way, what- 
ever difficulty there might be in drawing a line 
between knowing and reasoning, and reasoning 
and conjecturing, in certain instances, these 
operations might still be regarded as perfectly dis- 
tinct. 

Such a line, nevertheless, may I think be drawn 
in the former and principal of these cases, although 
it may not be altogether coincident with common 
phraseology. 



CONTINGENT REASONING. 27 

The doctrine of the preceding pages is, that 
Avhen our minds are determined by present facts, 
conjoined with experience or knowledge, to believe 
some fact past, absent, or future, we reason. 

From the sounds which at the moment of writ- 
ing I hear through the open window of my room, 
I am led to conclude that there is a lark warbling 
in the sky, although I am unable to see it. The 
printed page before me superinduces upon my 
mind the belief that, at some antecedent period, 
human beings put together the words and im- 
pressed the characters on the paper, although I 
have not the slightest information regarding the 
individuals who did so. In like manner, I feel 
assured that the buds on the rose-trees in the 
shrubbery will soon expand into full-blown 
flowers, and that the stone which I see a boy 
about to throw into the fish-pond will sink in the 
water. 

These according to the definition are all cases of 
reasoning. On examining them they all agree in 
this, that from something actually present to 
my senses conjoined with past experience, I feel 
satisfied that something has happened, or will 
happen, or is happening, beyond the sphere of my 
personal observation. 

The objection we are considering would go to 
maintain that these are not all cases of reasoning, 
but that some of them are cases of knowledge. 
li We know" it maybe said, " that the stone which 



28 THE THEORY OF REASONING. 

we hold in our hands will sink when thrown into 
the water ; we do not infer it." 

But may not the same be asserted with equal 
truth of the usual examples of reasoning given in 
logical treatises ? When it is argued that Peter is 
mortal (i. e. will die) because he is a man and all 
men are mortal, is not my knowledge or belief that 
Peter is mortal exactly on a level with my know- 
ledge or belief that a stone will sink in water? 
And if the former is a legitimate conclusion from 
premises or an inference, is not the latter equally so? 

It will be readily granted on all hands that what 
has taken place before my eyes I know. I know, 
for example, that I threw a stone yesterday into 
the water and that it sank : but with what pro- 
priety or correctness can I be said to know that the 
same stone will sink if I again throw it into the 
water to-day? And if this act of intelligence 
which regards an event that has not yet happened, 
is to be called knowledge, can I be said to know 
that a different stone will sink ? And if this is 
also to be called knowledge, can I be said to know 
that another substance which I have never tried, 
but which appears almost as heavy as stone, will 
sink too? 

Suppose the weight attenuated, suppose a number 
of substances presented to me varying from the 
weight of granite to that of cork, where in this de- 
scending scale of untried substances does know- 
ledge end, and inference or conjecture begin ? 



CONTINGENT REASONING. 29 

There appears to me to be only one solution of this 
difficulty and one line to be drawn. In philoso- 
phical strictness we can be said to know only those 
things which we perceive or have perceived through 
our organs of sense, and those states of mind or 
mental events of which we are or have been 
conscious. 

Other things we believe on evidence more or 
less cogent, that is to say, they are matters of in- 
ference : the only difficulty in the question seems 
to be, whether when we assume or think that the 
same identical properties which we have once per- 
ceived, are possessed continuously by the same 
identical thing, our intellectual state or act is to 
be termed inferring or knowing ? Whether, in the 
case already put, when I make sure that the same 
stone which I saw sink in the water yesterday, 
will sink again when thrown into the water to- 
day, I know the stone will sink, or I only infer it ? 
and this, when maturely considered, seems to be 
a question of terminology and not of fact. 

There are certainly reasons to be urged, al- 
though they are difficult to explain, why in this 
case we should use the term knowing. What do 
we mean by the expression " the same thing "? We 
mean a definite portion of matter possessing cer- 
tain perceptible qualities — a definite congeries in 
fact of such qualities. When, then, I feel sure of 
finding in future the same object to possess the same 
qualities as heretofore, it is only feeling assured 



30 THE THEORY OF REASONING. 

that a definite portion of matter will continue to 
be what it is — to continue in fact to exist. 

I perceive the properties of a piece of gold : I 
put it aside in my cabinet : when I take it out 
again, I rely upon the continued existence of those 
properties. It is the properties themselves which 
constitute the whole object. Knowledge of it can 
consist of nothing else than a cognizance of these 
qualities, and as I ascribe permanence to the ob- 
ject, I ascribe permanence to the qualities, the 
assemblage of which, in truth, forms the object, 
and I speak of them independently of reference to 
time. 

But even in this case there is an inference that 
the definite portion of matter continues unaffected 
by surrounding agents ; that is to say, without 
any addition or diminution, or any change of in- 
ternal structure. We may conclude that it con- 
tinues the same, from its not having, as far as 
appearances indicate, been exposed to the action 
of such agents ; but as these are often extremely 
subtle and imperceptible, we cannot know this. 
Instead of putting aside a piece of gold, I put aside 
a vessel of water : it is apparently protected from 
alteration internal or external; but the weather 
becomes colder, the temperature of the water falls, 
and although the liquid may appear the same to 
the eye, it has really undergone either a diminu- 
tion or enlargement of bulk. Its continuing there- 
fore to have the same properties is what I infer, not 



CONTINGENT SEASONING, 31 

what I know ; for if I consider it to have the same 
specific gravity as before I am in error. 

On these grounds, notwithstanding the instan- 
taneousness and certainty and familiarity of our 
intelligence in cases of this kind, they ought phi- 
losophically to be considered as cases of inferring 
and not of knowing. 

Whether this be considered a satisfactory view 
of the subject or not, it fortunately happens that 
the determination of the difficulty is of no prac- 
tical moment. There can be no great evil in con- 
founding knowledge and inference in cases where 
they are so hard to be distinguished, or rather 
where there is so little reason for preferring one 
term to another, and where, whatever name we 
give to the intellectual act, it is marked by so 
much promptitude and certainty. 

While on the one hand the conclusions of reason, 
when indubitable and familiar, are with difficulty 
distinguished from facts actually known, on the 
other hand it is not easy, according to the objec- 
tion before us, to distinguish them, when they are 
founded on doubtful premises, from what are called 
guesses or hypotheses. But in this case the solu- 
tion lies on the surface. We impose one name 
or the other according to the degree of evidence. 

When the grounds for believing any thing are 
slight, we term the mental act or state induced a 
conjecture ; when they are strong, we term it an 
inference or conclusion. Increase the evidence 



32 THE THEORY OF REASONING. 

for a conjecture, it becomes a conclusion ; diminish 
the evidence for a conclusion, it passes into a con- 
jecture. 

The process which ends in a conclusion and the 
process which ends in a conjecture are thus essen- 
tially the same, and differ only in degree or in the 
force of the evidence. A conjecture, therefore, if 
it has any grounds, is a species of conclusion : if it 
has none, it may be called a mere guess, a whim, 
or caprice or sally of the imagination, or any thing 
else implying disconnexion with proofs and pre- 
mises, which the reader may choose to term it, but 
it has no claim to the appellation of inference. 

After this discussion it is scarcely needful to 
combat the phraseology of Hobbes, who styles all 
that 1 have denominated contingent reasoning, 
conjecturing.* If the latter term were not con- 
fined to cases in which the grounds of inference 
are slight, all conclusions from historical facts 
would pass under the name of guesses, and the 
criminal found guilty of murder on circumstantial 
evidence might be said to be hanged on con- 
jecture. 

* Human Nature, chap. iv. 



DEMONSTRATIVE REASONING. 33 



CHAP. III. 

DEMONSTRATIVE REASONING. 

Let us turn, in the next place, to the second 
species of reasoning, in which certain things or 
facts lead us to discern other things or facts not 
immediately manifest by themselves. An example 
of it having been already given in the first chap- 
ter, and a still more detailed one being intended 
for the Appendix *, in order to avoid interrupting 
the exposition of the subject by too great particu- 
larity, the simplest instance will here suffice : the 
lines A and b are respectively equal to c, and 
therefore they are equal to each other. 

Here the mind observing successively the 
equality of a to c and that of b to c, is thence led 
to discern the mutual equality of A and b, which 
is not self-evident or immediately discernible from 
the inspection of A and b alone. 

It is plain that in reasoning of this second 
species, which is with great propriety termed de- 
monstrative, we intuitively discern, at each step, 
that one fact implies another, and discern too 
that a denial of the implied fact involves a con- 
tradiction. 

But demonstrative reasoning is not confined to 

* See Appendix, Article 1. 
D 



34 THE THEORY OF REASONING. 

the science of quantity. It is to be found in all 
departments of human knowledge. 

Whenever the mind discerns one fact to be im- 
plied in another, or the exclusion of a fact to be 
implied in another fact, it reasons demonstratively, 
whether they are facts of quantity or otherwise. 

Examples of this truth might be multiplied 
without end, but the few which follow will be 
sufficient for illustration. 

That portrait is a striking likeness of two dif- 
ferent persons ; therefore they must resemble each 
other. 

The two litigants cannot both be the exclusive 
owners of the property in dispute; therefore one 
of them must be urging a wrong claim. 

The traveller who was attacked had no money 
with him ; therefore he could not be robbed of a 
large sum as reported. 

The planets are opaque bodies ; therefore they 
must shine by light derived from an external source. 

Under this species of reasoning must be ranked 
that which is usually denominated syllogistic, but 
which I shall venture to call class-reasoning, be- 
cause perfect specimens of it, as I shall hereafter 
show, are found in the form of enthymemes. 

Of class-reasoning, or at least of so much of it 
as exemplifies the maxim of Aristotle, termed the 
dictum de omni et nullo, the characteristic is, in- 
ferring some attribute to belong or not to belong 
to a given individual or to given individuals of a 
class, because it belongs to all or does not belong 



DEMONSTRATIVE REASONING. 



35 



to any of the individuals of the class. It would 
be clearly a self-contradiction to admit the latter 
and to deny the former. All such reasoning is 
obviously demonstrative : it is, indeed, largely in- 
terfused in geometrical demonstration, in which 
general propositions not self-evident, but which 
have been shown to be implied in other proposi- 
tions, are subsequently employed as major pre- 
mises. Such, for example, are the propositions 
that the angles at the base of an isosceles triangle 
are equal ; that the three angles of every triangle 
are together equal to two right angles ; and that 
all equilateral triangles are equiangular. 

That all demonstrative reasoning consists in 
discerning, and, when expressed in words, in as- 
serting, one fact or one proposition to be implied 
in another, is plain. If we call one the implying 
fact, the other will be of course the implied fact, as 
in the following examples. 



IMPLYING FACTS. 

All horned animals are rumi- 
nant. 

The lines a and b are severally 
equal to c. 

The three angles of every tri- 
angle are together equal to 
two right angles. 

The culprit at the bar was in 
Edinburgh at one o'clock on 
the day named. 

The traveller had no money 
with him. 

The portrait resembles two 
different persons. 



IMPLIED FACTS. 

This horned animal is rumi- 
nant. 

The lines a and b are equal to 
each other. 

The three angles of the tri- 
angle abc are equal to two 
right angles. 

He could not be guilty of the 
offence committed at that 
time in London. 

He could not be robbed of a 
a large sum. 

They must resemble each 
other. 



d 2 



36 THE THEORY OF REASONING. 

By the terms implying and being implied nothing 
is assumed : they are merely expressive of the 
truth, that when the two facts so denominated are 
presented together to the mind, the proposition 
enunciating the second fact is at once seen to be 
true if the proposition enunciating the first is 
true, and the denial of it to involve a contradic- 
tion : nor is it pretended that this mode of stating 
an argument is superior for common purposes to 
the usual forms. 

If we examine the general principles on which 
demonstrative reasoning proceeds, or which it ex- 
emplifies, we shall find less uniformity than in the 
case of contingent reasoning. 

The general principle exemplified in the argu- 
ment, that a and b are equal to each other because 
they are respectively equal to c, is, that things 
equal to the same thing are equal to each other. 
In the demonstration cited in the first chapter, 
that the opposite angles made by the intersection 
of two right lines are equal, the reasoning con- 
sists of two steps, the first of which proceeds on 
the same axiom, while the second exemplifies the 
axiom, that if equals are taken from equals the 
remainders are equal. 

In the argument that because the culprit at the 
bar was in Edinburgh at a given time, he could 
not be guilty of a crime committed at that precise 
moment in London, the general principle exem- 



DEMONSTRATIVE REASONING. 37 

plified is, that a man cannot be in two places at 
the same time. 

Axioms might easily be educed in the same 
way from the other examples of demonstrative in- 
ference furnished in the preceding pages ; but as 
I purpose to resume the consideration of such 
maxims in a subsequent chapter, it would be 
superfluous to dwell upon them here. In that 
chapter, I shall enter into an express examination 
of the general principles exemplified in class-rea- 
soning, one of which has become so noted under 
the name of the dictum de omni et nullo. 

The remark before made regarding the cogency 
of the process in the first species of reasoning, 
may be repeated with regard to the second. Its 
cogency is not susceptible of proof. If the argu- 
ment that " because A and b are respectively equal 
to c they are equal to each other," is not intui- 
tively discerned to be true, nothing can make it 
appear so. It would be idle, too, in this case, as 
in the case of probable reasoning, to cite the 
general principle with a view to strengthen the 
force of the particular instance. The maxim that 
all things which are equal to the same thing are 
equal to each other springs up in the mind after 
the mutual equality of two particular things which 
are equal to a third thing has been discerned, and 
is merely a generalisation of what the particular 
fact implies ; a truth which will be more fully 
elucidated in the two following chapters. 

D 3 



38 THE THEORY OF REASONING. 

I have already remarked that all class-reasoning, 
or what is usually termed syllogistic, is in form at 
least demonstrative. This is, I believe, univer- 
sally allowed; but it has been objected against 
such reasoning that the major premise virtually 
contains the conclusion, and consequently every 
argument of the kind involves a petitio principii, or 
at least furnishes no real or no new inference.* 

What truth there is in this allegation, and 
whether, if true, it renders class-reasoning nuga- 
tory and useless, it may be instructive to examine. 
In this examination I shall confine myself at pre- 
sent to those cases of class- reasoning which ac- 
cording to a common logical distinction are de- 
monstrative, both in form and in matter, as I 
purpose in the next chapter to consider such as are 
really contingent, although bearing the semblance 
of demonstration. In order to simplify the dis- 
cussion, I shall also confine myself, as my prede- 
cessors have usually done, to such class-reasoning 

* See Campbell's Philosophy of Ehetoric, book i. chap, iv., 
and Stewart's Elements of Philosophy, vol. ii. p. 100. Des- 
cartes had long before made a similar observation. " To con- 
vince ourselves/' says he, " how little this syllogistic art serves 
towards the discovery of truth, we may remark that the 
logicians can form no syllogism with a true conclusion, unless 
they are already acquainted with the truth that the syllogism 
developes. Hence it follows that the vulgar logic is wholly 
useless to him who would discover truth for himself, though it 
may assist in explaining to others the truth he already knows." 
— Worhs byM. Cousin, vol. xi. p. 255., quoted by Mr. Hallam 
in his Literature of Europe, vol. iii. p. 260. 



DEMONSTRATIVE REASONING. 39 

as exemplifies the first half of Aristotle's maxim, 
viz. de omni, without expressly touching on such 
as exemplifies the second half, de nullo, or any- 
other maxims allied to the dictum. 

If it were intended to signify simply that the 
major premise implies the conclusion, the objection 
would allege as an imperfection what is the 
essential characteristic of all demonstrative reason- 
ing whatever ; inasmuch as in every case of it, one 
fact or proposition termed the premise, with or 
without the aid of another premise, as will be here- 
after explained, implies another fact or proposition 
termed the conclusion. If the first did not imply 
the second, i. e., if of the two facts, when viewed 
together, one were not discerned to be conclusively 
connected with the other, there could be no such 
thing as demonstration. 

But the objection is, that the major premise not 
merely implies but contains the conclusion ; that 
the conclusion is in reality a constituent or inte- 
grant part of the major premise, without which 
the latter would not be completely true. 

This allegation, it must be confessed, cannot be 
contradicted. The force of the reasoning in a 
demonstrative syllogism, or an enthymeme with 
a major premise, depends altogether on the fact 
expressed in the conclusion forming an integrant 
part of the general fact expressed in the major 
proposition, and consequently no new or unknown 
fact can ever appear as the inference. 

D 4 



40 THE THEORY OF REASONING. 

The essence of the conclusion, in such cases, 
consists in asserting that the subject of it does 
form an integrant part of the major premise. 

But although the allegation must be admitted, 
it does not by any means prove that such reasoning 
is nugatory or useless. It may, obviously, be of 
service to be reminded, or to remind others, or to 
have distinctly brought into view, that a given 
individual of a class possesses a certain attribute, 
when there is at the moment no other evidence to 
prove it, by citing the known or admitted fact, 
that all the members of the class possess it. 

As an illustration of this point, suppose I am 
engaged in the demonstration of a geometrical 
theorem : there is before me a complicated dia- 
gram containing, amongst several figures, a tri- 
angle which I have to compare with other figures, 
and, as a step in the reasoning, I have to show 
that the angles of the triangle in question are 
together equal to two right angles. I have not 
gone through the proofs with this particular tri- 
angle, but I call to mind that I have seen the 
proposition demonstrated of all triangles what- 
ever ; and from it, as an established truth, the con- 
clusion that the angles of the triangle in the 
diagram, although not expressly investigated, are 
together equal to two right angles, irresistibly 
follows. It is simply thinking or saying " in all 
triangles the three angles are equal to two right 
angles, and of course the particular triangle before 
us is included in the general fact." 



DEMONSTRATIVE REASONING. 41 

Whether the declaration or recognition of such 
a contained fact is to be termed an inference or 
not, seems to be a question of phraseology. 

I am myself disposed to think that any fact 
which can be shown to be implied or contained in 
another fact, may be conveniently and properly 
said to be inferred from it, and that the process 
may be with equal convenience and propriety 
termed reasoning. It is true that on this plan 
many implied facts, when expressed in words, 
would assume the appearance of fruitless and 
frivolous inferences, and seem, as the phrase is, 
" not entitled to the name." But a similar re- 
mark might be made with regard to many other 
convenient designations. We give the name pro- 
position, for example, to any expression which 
affirms or denies one thing of another * ; and far 
from withholding it from trite and flat phrases 
and truisms, we constantly speak of puerile, nuga- 
tory, and identical propositions. In the same 
manner we talk of bad poetry and wretched 
painting, although the critic in his righteous in- 
dignation may cry out, Do you call this poetry ? 
it is sheer rant ; Do you dignify this with the 
name of painting ? it is a mere daub. It would be 
in analogy with these examples to apply the term 
inference to any proposition before which we can 

* UpOTCMTLQ jieV OVV SffTL XoyOQ KCLTCKfiaTlKOQ 1) CLTTO^aTlKOQ Tlt'OS 

Kara rivog. — Aristotelis Analytic. Prior, lib. 1. 



42 THE THEORY OF REASONING. 

properly use the word therefore, marking our sense 
of its low character when requisite by such epi- 
thets as useless or frivolous. Of this description 
would be the logical trifling sometimes cited, — 

All men are fallible ; 

Therefore some men are fallible. 
But there are other propositions prefaced by 
therefore which, although generally banished from 
the rank of conclusions, or regarded as mere ex- 
amples of conversion, might be classed amongst 
the really useful inferences ; e. g., 

No man is infallible ; 

Therefore no infallible being is a man. 
All instances of the conversion of propositions, 
indeed, are really instances of demonstrative rea- 
soning. They are pure enthymemes which re- 
quire no major premises, although it is perfectly 
practicable, as it is perfectly useless, to throw them 
into the full syllogistic form. Of this I shall fur- 
nish proof in a subsequent chapter on the forms 
in which the operations of reasoning may be ex- 
pressed. 

The last example, in truth, represents a class of 
demonstrative inferences exceedingly common, 
where the same fact is presented in two different 
aspects, or approached by the mind in two oppo- 
site directions, and an assertion is made that be- 
cause it is true in one aspect, it is true in the 
other. 



DEMONSTRATIVE REASONING. 43 

These two aspects are sometimes positive and 
negative, as, 

The man we are speaking of is enslaved by his 

appetites ; 
Therefore he is not free. 
They are sometimes active and passive, as, 

The Duke of Wellington vanquished Bonaparte; 

Therefore Bonaparte was vanquished by the 

Duke.* 

Sometimes such inferences amount to little more 

than varieties in the expression of the same fact, 

and many of them undoubtedly seem puerile, but 

they are demonstrative, and, notwithstanding their 

apparent puerility when standing alone, they are 

often convenient stepping-stones in argumentative 

discourse, when their trivial character is merged in 

their transitional utility. f 

All these we may rank amongst convenient and 
useful inferences, and with equal reason we may 
place in the same class such as we have been en- 
gaged in discussing — those, namely, of really de- 
monstrative syllogisms — notwithstanding the un- 

* A. modern author, in reference to a similar example, says, 
" We either think that Philip was beaten by Peter, or that 
Peter beat Philip ; two distinct thoughts, though relating to one 
fact. In reading from the tablet of our mind, we may bring 
forward the images in one order, or in another." — Outline of 
the Laws of Thought, p. 109. 

f For some actual examples of such inferences as are here 
described, see Examination of a passage from Burke in the 
Appendix, Article 1. 



44 THE THEOEY OF REASONING. 

deniable fact that the conclusion is always contained 
in the major premise. 

The admission of this truth detracts, it must be 
owned, from the importance of demonstrative class- 
reasoning as it stands in general estimation, and 
circumscribes such reasoning within very narrow 
boundaries. 

It is an obvious reflection, that if no fact can be 
inferred in syllogistic reasoning but what is con- 
tained in the major proposition, no science can 
possibly be constructed by a series of real or legi- 
timate syllogisms alone. Hence there must be a 
fallacy in the assertion that the science of Geometry 
can be exhibited in such a series. This feat has, I 
am aware, been ostensibly accomplished, and the 
way in which it has been performed presents no 
difficulty * ; but, as I shall hereafter have occasion 
to show, it has been done solely by the intro- 
duction of redundant propositions, merely incum- 
bering the demonstration, and disguising the real 
source of the validity of those arguments into 
which they are so unavailingly intruded. Such 
syllogisms may be fairly termed spurious. 

* In Stewart's Elements, vol. ii. p. 260, it is stated that the 
first six books of Euclid had been exhibited in syllogisms by 
two writers named Herlinus and Dasypodius. See also Sir 
Wm. Hamilton's Edition of Reid's Works, p. 702, where the 
same fact is mentioned. 



INDIRECT CONTINGENT REASONING. 45 



CHAP. IV. 

CONTINGENT UNDER THE FORM OF DEMONSTRATIVE 
REASONING. 

I have now taken a survey of contingent and 
demonstrative reasoning, and endeavoured to show 
the nature and cogency of each species, and also 
the general principles on which they proceed or 
which they exemplify. 

But I have still to notice a large class of cases in 
reasoning which partake of the character of both ; 
which, while they are contingent in reality, are 
demonstrative in form. 

It has been already explained that the formation 
of general laws, extending beyond the observed 
facts from which they are derived, is, in every 
instance, an act of contingent reasoning ; that 
general laws rest on the same evidence or are de- 
duced from the same premises as particular in- 
ferences. 

It is, nevertheless, a common and often a very 
convenient practice, first to deduce the general 
law, and afterwards from the general law to draw 
the particular inference, which then wears the ap- 
pearance of a demonstrated truth. 



46 THE THEORY OF REASONING. 

The subject may be elucidated by an instance of 
reasoning similar to one before given. 

All human beings, as far as observation has 

extended, have been found fallible ; 
Therefore the unknown author of the book 
just put into my hands is fallible. 
This, which is a good material argument, an 
instance of forcible contingent reasoning, may be 
converted into the following demonstration by as- 
suming as a major premise the general law which 
is deducible from the preceding uniform fact. 
All human beings are fallible ; 
Therefore the author of this book is fallible. 
It is obvious, nevertheless, that the real nature 
of the reasoning cannot be altered by changing 
the form in which it is expressed. The evidence 
of the fallibility of human beings consists in pre- 
vious known instances of the intellectual qualities 
exhibited by them ; and the conclusion drawn from 
these instances is as to the intellectual qualities of a 
writer concerning whom we know nothing. The 
process is really inferring from what has existed in 
all similar, i. e. all other cases, what exists in this 
case. 

As a further illustration, let us examine a piece 

of reasoning often cited in logical treatises. 

All horned quadrupeds are ruminant ; 

Therefore this horned quadruped is ruminant. 

Whether we take this enthymeme as it is, or 

make it, by the introduction of a minor premise, 

into a regular syllogism, the conclusion drawn is 



INDIRECT CONTINGENT REASONING. 4< 

irresistible. You cannot admit the premise and 
deny the conclusion, without self-contradiction. 

But the form into which the reasoning is. thrown 
by using the general law as a major premise masks 
the real nature of the evidence for the conclusion. 
The real argument is, 

All other horned quadrupeds have been found 

to be ruminant ; 
Therefore this horned quadruped is ruminant. 

It is because we have found horned quadrupeds 
to have been ruminant in all other cases, as far as 
our knowledge has extended, that we conclude 
that the horned animal before us is ruminant. The 
fact or collection of facts gathered from observation 
without any contrary instance, is sufficient to de- 
termine the mind to believe the conclusion ; but 
there would be no self-contradiction, although a 
want of sound sense, in admitting the premise and 
denying the inference. The reason is not what is 
usually designated logical or demonstrative, but 
material or contingent. It is, nevertheless, all that 
we can possibly have in the case. 

Laying down the general law, that all horned 
quadrupeds are ruminant, has not the slightest 
power to change either the character of the facts 
of which it is the indication, or that of the conclu- 
sion to which it may lead. Material arguments 
cannot be converted into demonstrative proofs by 
any arrangement of propositions, or by any trans- 
lation from one form into another. 



48 THE THEORY OF REASONING, 

In these observations, I do not of course intend 
to assert that we ought never to make our in- 
ferences from such general propositions, for there is 
obviously a natural tendency in the human mind 
to do so, and an indispensable convenience in the 
practice. I simply maintain that they do not in- 
crease, or strengthen, or alter in any way, the real 
force of the proofs. Being conclusions of precisely 
the same nature, and resting on the same evidence 
as the particular conclusions sought to be demon- 
strated by them, it follows that no force can be 
derived from them to the latter. * 

Perhaps it would be a useful way of marking 
the distinction between these two modes of con- 
tingent reasoning, to call one the direct and the 
other the indirect. 

The difference might be illustrated and exhibited 
to the eye in a diagram, where the point or angle 

a denotes the collective fact ; 

b ,, the general law ; 

c „ the particular inference. 
Supposing the distances between 

the points to be equal, or, what is 

the same thing, the triangle to be 
equilateral, it is obvious that if you proceed in 
a straight course from a, you may get to b or to c 
with equal readiness ; but you may also get to c 

* This argument has been forcibly put by Mr. John Mill, in 
his valuable System of Logic. See vol. i. p. 250. 




INDIRECT CONTINGENT REASONING. 49 

by first going from a to b, and then from b to c : 
the first would be the direct way, the second the 
indirect. So, inferring from the collective fact " all 
men have hitherto been found fallible " (a), that 
this man is fallible (c), would be a direct inference 
from the evidence, as would be also inferring from 
the same collective fact that all men are fallible (b) ; 
but inferring from the general law " all men are 
fallible " that this man is fallible, although direct 
if no reference is made to the original ground, 
would be an indirect way of deducing the particular 
inference from the pristine evidence on which it 
rests : it would be going from A to c via b. 

It often happens, indeed (to pursue the parallel) 
that we find ourselves at b, and then, if we want to 
proceed to c, it would be roundabout to retrace our 
steps first to a. When we have already reached a 
general law, we may safely and usefully deduce 
conclusions from it, without the constant necessity 
of re -ascending to the original evidence.* 

It follows, nevertheless, that the universal law, 
which is itself merely an inference in contingent 
reasoning, cannot be rightly employed, as a de- 
monstrative major premise to prove a particular 
conclusion, without what may be called a logical 
reservation. The conclusion is not, in reality, a 
necessary consequence of the evidence, although 

* It is scarcely necessary to say that the diagram above in- 
troduced is not intended to prove any thing : it is merely an 
attempt to place the subject in a clear light. 

E 



50 THE THEOKY OF REASONING. 

the shape into which the argument is thrown will 
make it appear such ; and deducing it from the 
universal law can be considered only as a form of 
which it is frequently convenient to avail ourselves, 
but in using which, we should never forget the 
contingent character of the argument. In effect, 
if we closely scrutinise the subject, we shall find 
that the only kinds of general propositions which 
can be legitimately regarded as implying individual 
facts, and thus employed absolutely as demon- 
strative premises, are two, namely, such as are 
formed from a complete knowledge or discernment 
that the predicate is true of every individual of the 
class (which embraces the enumeratio plena of logi- 
cians), and such as are rigidly deduced from incon- 
trovertible data. An example of the former may 
be seen in the propositions, " all the planets are 
opaque bodies," " all murders are punishable by 
death ; " of the latter, in the theorem " all equilateral 
triangles are equi-angular. 

In all other cases, however forcible, or well-es- 
tablished, or undeniable the general law maybe, the 
reasoning in which it is employed as a major pre- 
mise, although demonstrative in form, comes under 
the description of contingent reasoning, and can 
be correctly regarded in no other light. 

From all this, the necessity of knowing the pre- 
cise signification of the terms used in class-reason- 
ing before we can determine the real nature of the 
inference drawn, is an obvious corollary. 



INDIRECT CONTINGENT REASONING. 51 

But the most important application of this view 
of the subject, is that it enables us to see how com- 
pletely such apparently demonstrative reasoning 
escapes the objection brought against syllogistic 
arguments, and adverted to in the last chapter, 
that the major premise virtually contains the con- 
clusion, and that, consequently, the argument in- 
volves a petitio principii, and furnishes no real in- 
ference. 

Many minds have been perplexed in attempting 
to reconcile the admitted truth, that the conclusion 
forms an integrant part of the general proposition 
from which we set out, with the equally acknow- 
ledged truth that from such propositions we deduce 
unobserved facts, not really included in the major 
premise. 

But the view of the subject here presented re- 
moves the whole difficulty. Whatever weight the 
allegation of & petitio principii may have in the case 
of purely demonstrative class-arguments, it can 
have no application to such as we are here treating 
of, when thrown back into their pristine form. 
Although it may lie against an argument in the 
shape of 

All men are fallible, 

Therefore this man is fallible, 
it cannot for a moment be brought against one in 
the shape of 

All other men have been fallible, 

Therefore this man is fallible, 

E 2 



52 THE THEOBY OF REASONING. 

which is the true type of contingent reasoning from 
collective facts or general propositions. 

In this latter case, all semblance of petitio prin- 
cipii vanishes : the difficulty is cleared up ; a fact 
is inferred which has not been observed and is not 
included in the premise. And as the greater part 
of our reasoning from general propositions respect- 
ing the events around us, material and moral, is 
of this character, however it may wear the guise 
of demonstration, the objection before us, as al- 
ready intimated, can at the utmost have only a 
comparatively limited application, viz. to deduc- 
tions from such general propositions as can alone 
be employed absolutely as demonstrative major 
premises. 

Perhaps the subject may be rendered clearer to 
some readers by the following dialogue. 

A. It is surely demonstrative reasoning when I 
conclude that this man is fallible because all men 
are fallible. 

B. That is to say, because every individual man 
is fallible. 

A. Of course. 

B. In asserting every individual man to be fal- 
lible, do you include this man or do you not ? 

A. I include all men, and him amongst the rest. 

B. Then your argument is this, " Every indi- 
vidual man, including this man is fallible ; therefore 
this man is fallible:" in other words, you argue 



INDIRECT CONTINGENT REASONING. 53 

that this man is fallible because he is fallible, which 
is certainly demonstrative enough. 

A. Of course the reason really meant to be as- 
signed is, that all other men, as far as observation 
has extended, have been found to be fallible. 

B. That is to say, all men, excluding this 
man, have been found to be fallible, therefore this 
excluded man is fallible. Now this is a good 
material or contingent reason, but it is not a de- 
monstratively conclusive one. In the case of every 
demonstrated truth, the opposite or negative pro- 
position would be a contradiction in terms. That 
this man is not fallible would be a contradiction to 
the proposition that all men are fallible, but not 
to the proposition that all other men are fallible. 
Thus, if you include this man you beg the ques- 
tion : if you do not include him your reason is a 
material or contingent one, very highly probable, 
engendering almost complete certainty, but not 
demonstratively conclusive. 

What has been said in this chapter may appear 
on a first glance to correspond with the well- 
known distinction made by Aristotle between de- 
monstrative and dialectical syllogisms ; but there 
is a fundamental difference, which it may be well 
to note. His words are, " The syllogism is a form 
of language in which certain things being laid 
down, another thing different from those laid down 
necessarily results from them. Now demonstra- 
tion takes place when a conclusion is drawn from 

E 3 



54 THE THEORY OF REASONING. 

things true and primary, or from those of which 
the knowledge has been derived from the true and 
primary. But in a dialectical syllogism, the con- 
clusion is drawn from probable things. The true 
and primary are such things as are believed of 
themselves, and not on account of other things : for 
it behoves not that in the principles of a science 
the reason why should be sought for, but every 
principle should be certain in itself." * 

This is in truth merely saying that when the 
premises are only probable, the conclusion will be 
so too, and giving the appellation of dialectical to 
syllogisms in which they occur. 



* "Eoti Srj (TvXXoyLfffxoQ Xoyog kv <o teQevtojv tivu>v erepov tl 

TU)V KElfJLEVUV, El, ClVayKrjQ GVJlt>aivEl Zdl TU)V KELjJLEViOV. ' 'A7T oh El^lQ 

jjlev ovv karlv, orav it, aXrjdiov /ecu irpwriov 6 avXXoyiffjioQ i], rj ek 
toiovtojv a diet tlvojv 7rpojTU)v teal aXrjdCJv rfjg TTEpX avra yvioGEwg 
ttiv ap^jiv e'lXtj^ev * dia\EKTLKog Se avXXoyiafJLOQ 6 l£ kvdol^iov 
ffvXXoyt^ofjLEvog. "Eon 3e ak^Qi) jxev kol 7rpwra ra firj cV kripiov 
ctXXa cV avrujv EyovTa rrjv tt'iotiv ' ov ^eT, yap kv tcuq E"KKTTr\\io- 
vuzcuq apyaig ETri£r)TEl<rQcu to Slcl ti, aXX' t/caorr/v tHjv ap^wv 
avrrju »ca6' kavrfjv Etvai TciaTi]v. — Topicorum lib. i. cap. 1. 

The same point is thus explained by Wallis. 

" Syllogismus Topicus (qui et Dialecticus dici solet, et Dida- 
scalicus) talis haberi solet syllogismus (seu syllogismorum 
series) qui firmam potius praesumptionem, seu opinionem valde 
probabilem creat, quam absolutam certitudinem. Non quidem 
ratione formes (nam syllogismi omnes, si in justa forma, sunt 
demonstrativi ; hoc est, si prsemissas vera sint, vera erit et con- 
clusio), sed ratione materia? seu praemissarum ; quas ipsae, ut 
plurimum, non sunt absolute certae et universaliter verae ; sed 
saltern probabiles, atque ut plurimum vera?." — Institutio Logi- 
cce, lib. iii. cap. 23. 



INDIRECT CONTINGENT REASONING. 55 

But this is not all that is maintained in the pre- 
sent chapter, nor even the material part of it. 

My doctrine is, that all such reasoning as con- 
sists in inferring unobserved facts from general 
propositions, although strictly demonstrative in 
form, is in reality contingent, how certain and 
indisputable soever the general propositions may 
be ; and that it is represented by the formula, 
All other men have been found fallible ; 
Therefore this man (whose fallibility has never 
been observed) is fallible. 

According to my view, consequently, many syl- 
logisms would rank in the class of arguments 
demonstrative in form but contingent in reality, 
besides those which, in the popular use of the 
term probable, have only probable premises. If I 
understand Aristotle aright, the latter alone would 
fall under his denomination of dialectical. 

It has been well observed by Mr. Stewart in re- 
ference to this distinction in the first book of the 
Topics, that there is an impropriety in such an 
employment of the epithets demonstrative and dia- 
lectical, inasmuch as it implies, or seems to imply, 
that one species of syllogism may be more con- 
clusive and cogent than another*, which is at 
variance with Aristotle's own doctrine in other 
places, and of course was not intended here. 

* Elements of the Philosophy of the Human Mind, vol. ii. 
p. 262. 8vo. ed. 

E 4 



56 THE THEORY OF REASONING. 



CHAP. V. 

THE INTERMIXTURE OF CONTINGENT AND DEMON- 
STRATIVE REASONING. 

It seems necessary, in order to complete our sur- 
vey of the two great divisions of the subject, to 
advert more particularly to a circumstance already 
indicated in some of the examples introduced into 
the preceding exposition ; viz. that demonstrative 
reasoning, even when non-syllogistic, is by no 
means confined to mathematics or the science of 
quantity ; but it is perpetually intermixed with 
contingent reasoning on matters of a moral or a 
physical nature. 

This might be exemplified by a thousand in- 
stances in common life. Take, for example, the 
course pursued by an advocate in defending his 
client from a criminal accusation. If he relies, as 
he is sometimes compelled to do, upon testimony 
to his client's character, the argument is purely 
contingent : he attempts to establish the moral 
excellence of the man, and then infers that a per- 
son of such estimable qualities would not be likely 
to commit the offence of which he is accused. But 
if, instead of this, he endeavours to prove an alibi, 
the logical procedure is altered. The crime (we 
will suppose) was committed in London, and he 



INTERMIXTURE OF ARGUMENTS. 57 

produces several credible witnesses who swear, 
that at the very moment when the deed was per- 
petrated, they saw the accused in Edinburgh. In 
this hypothetical case, the reasoning of the defence 
is mixed. When from the number, and respecta- 
bility, and concurrence of the witnesses the advo- 
cate infers that their testimony is true, he employs 
a contingent argument ; but when he proceeds 
further, and concludes from the attested fact of his 
client's being in Edinburgh that he could not have 
committed a crime at the same moment in Lon- 
don, this step in the reasoning is demonstrative. 

We may observe a similar intermixture of rea- 
soning on very various occasions, and, amongst the 
rest, on the common occasion of making indirect com- 
parisons between objects and qualities of all kinds. 

If two substances, for example, which could not 
be brought into juxtaposition, are attested to have 
been successively compared with a third substance 
and found to be respectively of the same colour 
with it, we conclude that they agree in colour with 
each other. 

In this case, while the inference that the two 
mutually unapproachable substances are each of 
the same colour with the third (resting as it does 
on testimony) is contingent, the conclusion that 
therefore the two former substances resemble each 
other in colour, is necessary. A demonstrated 
conclusion, however, from a premise which has 
been obtained by contingent reasoning, must itself 



58 THE THEORY OF REASONING. 

participate in the uncertainty of the premise. A 
chain (as some one has well observed in elucida- 
tion of this point) may be composed of both strong 
and weak links, but its strength, as a chain, can 
never be greater than that of the weakest link 
in it. 

The way in which even strictly mathematical 
reasoning — reasoning about quantity — occurs in 
treating of matters of fact is familiar to the stu- 
dents of natural science, and may be illustrated by 
a short passage from a physiological writer whose 
arguments are frequently close and cogent. 

"In the young of the carnivora," he says, " the 
weight [of the body] does not remain unchanged ; 
on the contrary it increases from day to day by an 
appreciable quantity. This fact presupposes that 
the assimilative process in the young animal is 
more energetic, more intense, than the process of 
transformation in the existing tissues. If both pro- 
cesses were equally active, the weight of the body 
could not increase ; and were the waste by trans- 
formation greater, the weight of the body would 
decrease." * 

This is obviously a strict demonstrative argu- 
ment. We see intuitively that if the body gains 
weight, more matter must be added to it than 
is subtracted from it. 



* Animal Chemistry, by Justus Liebig, edited by Dr. 
Gregory, p. 67. 



INTERMIXTURE OF ARGUMENTS. 59 

To these examples of the intermixture of one 
species of reasoning with another, may be added 
the frequent introduction into argumentative dis- 
course of other demonstrative enthymemes such as 
I have described in the third chapter, and for in- 
stances of which the reader may consult the 
Appendix.* 

It may be remarked further, that the several 
varieties of demonstrative reasoning, as distin- 
guished by the general principles which they ex- 
emplify, are to be found intermingled both with 
contingent reasoning and with each other. In 
geometry, as it is almost needless to mention ex- 
cept to recall the fact to the mind of the reader, 
we often find that in the demonstration of a single 
theorem, two or three different axioms are succes- 
sively exemplified. 

* Article, No. 1. Examination of a passage from Burke. 



60 THE THEORY OF REASONING. 



CHAP. VI. 

PRINCIPLES OF REASONING OR MAXIMS, AND 
ESPECIALLY THE DICTUM OF ARISTOTLE. 

Although in the preceding chapters it was im- 
possible not to touch incidentally on the place 
which axioms hold in reasoning, or rather in re- 
lation to it, yet, on account of the erroneous notions 
still prevalent in regard to them, notwithstanding 
what has been said by Locke in his chapter on 
maxims, and by Stewart in the 2d volume of his 
Philosophy, it may be useful to renew and ex- 
tend the discussion of the subject. It will not be 
requisite to take into express consideration at the 
same time the analogous general principles of con- 
tingent reasoning, because any deficiency in my 
previous explanation of their character will be sup- 
plied by many of the following remarks, which 
?nutatis mutandis will apply to them. 

In demonstrative reasoning maxims or axioms 
are nothing more or less than self-evident general 
propositions formed from particular arguments, 
and every instance of demonstration may be ranged 
under some one or other of them as exemplifying 
it. If we take a few of the implying and implied 
facts adduced in the last chapter, this will be suf- 
ficiently manifest. 



PRINCIPLES OF REASONING. 



61 



General Principle or Maxim. 

Things equal to the same thing 
are equal to each other. 



A man cannot be in two places 
at the same time. 



If equals are taken from equals, 
the remainders are equal. 



Arguments. 

Implying fact : The lines a and 

b are severally equal to c. 
Implied fact : The lines A and 

b are equal to each other. 
Implying fact : Juvenis was in 

Edinburgh at noon on the 

day named. 
Implied fact : He could not be 

guilty of an offence com- 
mitted on that day and at 

that hour in London. 
Implying fact : The angles abd 

and abc are together equal 

to the angles abd and a be. 
Implied fact: The angle abc 

is equal to the angle a be. 

Here it is obvious the maxims are only gene- 
ralisations of the particular arguments, or of the 
particular instances of implication ; and the self- 
evidence of both maxims and arguments is on a 
level, although the priority in respect of origin is 
with the latter. 

In reference to these general principles or 
maxims, a variety of phrases are employed : thus, 
by some philosophers an argument is said to pro- 
ceed on a certain general principle ; by others, to be 
an application of it, to rest or to be founded upon 
it. The general principle itself is affirmed to be 
implied in the argument, to be involved in it, to 
be essential to it ; while the conclusion is asserted 
to be dependent on the general principle, or 
to be proved by it or in virtue of it. These 
different expressions, when they are not posi- 



62 THE THEORY OF REASONING. 

tively erroneous, fail to describe with precision the 
real place occupied by these maxims in relation to 
the reasoning process. They can have, neverthe- 
less, only one legitimate meaning. The correct 
and most precise mode of stating the matter is to 
say, in respect of any particular argument, that it 
is an exemplification of a certain general principle 
or maxim ; and in respect of the general principle, 
that it is exemplified in the particular argument, or 
is a generalisation of it, or may be educed from it. 

The phraseology which implies that a conclusion 
is proved by any of these maxims, or in virtue of 
them, or is dependent upon them for its validity, is 
especially objectionable. In each of the instances 
of implication quoted above, the second fact or 
proposition is intuitively discerned to be implied in 
the first, as soon as both are viewed together ; and 
this discernment of the particular truth is not at all 
dependent on the general maxim, which is, indeed, 
logically the result of subsequent discernment. It 
would be more correct to say that the general prin- 
ciple is deduced from the particular truth, than, 
conversely, that the particular truth is deduced 
from the general principle. 

The latter statement is, indeed, wholly erroneous. 
These maxims have no probative force ; they add no 
cogency to any argument ; the conclusion does not 
at all depend upon them : they merely present the 
particular argument in a generalised form; a form 
which can be reached only through the particular 



PEINCIPLES OF REASONING. 63 

argument which may happen to be before us, or 
another similar to it. 

Speaking of such self-evident truths, Locke re- 
marks, • ■ they are known in particular instances 
before these general maxims are ever thought on, 
and draw all their force from the discernment of 
the mind employed about particular ideas."* 

Mr. Stewart, who concurred in this view with 
the illustrious author of the Essay on Human 
Understanding, gives the following lucid exposi- 
tion of his doctrine. 

u It was long ago remarked by Locke, of the 
axioms of geometry as stated by Euclid, that al- 
though the proposition be at first enunciated in 
general terms, and afterwards appealed to, in its 
particular applications, as a principle previously 
examined and admitted, yet that the truth is not 
less evident in the latter case than in the former. 
He observes further that it is in some of its par- 
ticular applications, that the truth of every axiom 
is originally perceived by the mind ; and, there- 
fore, that the general proposition, so far from 
being the ground of our assent to the truths which 
it comprehends, is only a verbal generalisation of 
what, in particular instances, has been already 
acknowledged as true." f 

* On the Understanding, book iv. chap. vii. § 4. 
t Elements of the Philosophy of the Human Mind, vol. ii. 
p. 29. 2d ed. 



64 THE THEOKY OF REASONING. 

Another writer, eminent both as a mathematician 
and a philosopher, I mean D'Alembert, gives his 
sanction to the same view, and remarks, that so 
far are axioms from holding the first rank in phi- 
losophy, that there is no necessity even to enun- 
ciate them. He afterwards terms them barren 
and puerile truths.* 

Taking with us these considerations regarding 
the value and position of self-evident maxims, let 
us turn to the celebrated dictum of Aristotle. 

The dictum de omni et nullo, viz. that " whatever 
is predicated universally of any class of things, 
may be predicated in like manner of any thing 
comprehended in that class," is not only stated by 
logicians to be a general maxim, of the applica- 
tion of which every direct syllogism is a particular 
instance, but proclaimed to be the universal prin- 
ciple of reasoning. 

If we closely scrutinise the meaning of this 
maxim, undazzled by the somewhat magnificent 
and imposing phraseology in which it has been 
spoken of, we shall find it an obviously simple 
and undeniable proposition, namely, whatever is 
asserted of a class may be asserted of any species 
or individual of that class. A class, however, 
we must bear in mind, is not a collective or 
corporate whole, which, as a whole, possesses pro- 

* Elemens de Philosophic, chap. iv. ; also Discours Pre- 
liminaire de l'Encyclopedie. 



PRINCIPLES OF REASONING. 65 

perties or attributes different from those of the in- 
dividuals composing it ; but what is predicated of 
it is predicated of every separate individual ranked 
under it. The proposition " all men are fallible " 
affirms that every individual man is fallible, while 
the proposition " the army is large " affirms of the 
body collectively something which it does not af- 
firm of any single individual in it. If a class were 
such a collective body, the Aristotelian maxim 
could not be true.* 

The dictum, therefore, it is plain, means neither 
more nor less than that whatever is predicated of 
every individual of a class may be predicated of 
any individual, or any number of individuals of 
that class. As, however, what can be truly pre- 
dicated of any thing must be a property or attri- 
bute actually possessed, we may, if we choose, 
leave out predication altogether, and then the 
maxim will appear in a still simpler shape, as fol- 
lows : What belongs to every individual of a class 
must belong to any individual of that class. How- 
ever it may be expressed, it is obviously a self- 
evident and indisputable truth, like the other 
maxims we have just been considering; and this 

* Lord Karnes was sharply taken up by Dr. Gillies for 
having blundered on this point, he having represented the 
dictum to be, " Whatever is true of a number of particulars 
joined together, holds true of every one separately " — See 
Aristotle's Ethics and Politics, translated by John Gillies, 
LL.D., vol.i. p. 76. 

F 



66 THE THEORY OF REASONING. 

view of its co-ordinate character is sufficient of itself 
to determine the accuracy of the doctrine which 
proclaims it as the universal principle of reasoning. 

To this point I must draw the reader's par- 
ticular attention, for here lies the grand error of 
the Aristotelian theory ; and it is really astonishing 
that a mistake of such magnitude should have been 
so implicitly admitted. 

If the doctrine were true, every act of reasoning 
would be an exemplification of this one maxim, 
and might be ranged under it : in other words, 
all reasoning without exception would consist in 
concluding that an attribute belongs to some in- 
dividual of a class *, because it belongs to every in- 
dividual of that class. No other reason, according 
to this theory, can possibly exist or be assigned. 
The sole ground on which we can argue that an 
individual thing possesses any attribute is, that 
the thing belongs to a class all the members of 
which possess the attribute. The only kind of 
implication possible consists in generic facts im- 
plying individual facts. 

In contradiction to all this, it has been shown 
above, that there are many other general principles 
or maxims of which particular acts of reasoning 
are exemplifications ; such as, " things equal to 

* Or is excluded from it. I have thought it needless to take 
into separate consideration the de nullo part of the maxim, as 
it would lead only to repetitions : negative propositions may, as 
Mr. Walker says, be considered at pleasure as affirmative. 



PKINCIPLES OF REASONING. 67 

the same thing are equal to each other;" " a body 
cannot be in two places at one time ; " "if equals 
are taken from equals the remainders are equal." 
When I affirm that two things, A and b, are equal 
to each other because they are severally equal to 
c, or that a man could not commit a crime at a 
specified time in London because he was at that 
precise moment in Edinburgh, I reason just as 
much as I do when I affirm that this man is fal- 
lible because all men are fallible, or that the three 
angles of the triangle before me are together equal 
to two right angles, because the three angles of 
every triangle are equal to two right angles. 

The dictum, then, is obviously one of those self- 
evident maxims which we have above described, 
and it may be exhibited in the same manner. 

Arguments. 

Implying fact : All horned 



General Principle. 

Whatever is predicated of a 
class may be predicated of 
any individual of that class. 



animals are ruminant. 
Implied fact : This horned 

animal is ruminant. 
Implying fact : The three The same. 

angles of every triangle are 

together equal to two right 

angles. 
Implied fact : The angles of 

this triangle are together 

equal to two right angles. 

If we compare these instances of one fact or 
proposition implying another with the others al- 
ready referred to, we shall at once discern the 
true place and value of this renowned maxim ; we, 

F 2 



68 THE THEORY OF REASONING. 

shall see that the dictum de omni et nullo is a cor- 
rect expression of the general principle on which 
some acts of reasoning proceed, or, in more correct 
language, which they exemplify ; but that, in this 
respect, it is only on a level with other maxims, 
such as have been cited. 

It may possibly be alleged, that at any rate one 
of the instances cited above as exemplifying an- 
other maxim may be ranged under the dictum of 
Aristotle. Drawn out at full length (it may be 
said) the argument in question is as follows : 

All things equal to the same thing are equal 

to each other; 
a and b are equal to the same thing c, 
Therefore they are equal to each other. 
Here, it may be urged, a and b are argued to 
be equal to each other, because they belong to the 
class of things which are equal to the same thing ; 
but, as I shall have occasion to show again when 
treating of the syllogism, it is not because they 
belong to any class that we conclude them to be 
equal, but it is on account of the particular fact 
of their being respectively equal to c. Strike out 
all reference to a class, expunge the whole of the 
major premise, chain down the mind to this single 
instance of equality, and still the reasoning is 
complete, and the conclusion remains perfectly un- 
disturbed. This argument, consequently, is no 
exemplification of the scholastic maxim. It shows 
conclusively that ratiocination is not so limited 



PRINCIPLES OF REASONING. 69 

and insignificant as to consist in nothing else than 
concluding an attribute to belong to an individual, 
because it belongs universally to the class of which 
that individual is a member.* Eeason refuses to 
be tethered to the stake of the dictum. 

Logicians themselves, moreover, admit (some of 
them at least), that the dictum de omni et nullo is 
not intended or adduced to prove the force of syl- 
logistic reasoning, for that would be attempting to 
demonstrate the validity of demonstration ; but it 
is to be considered merely as a generalised state- 
ment of all demonstration whatever. In a manner 
quite analogous, the maxim which appears as the 
major premise in the above syllogism, viz. " all 
things equal to the same thing are equal to each 
other," is to be considered as a generalised state- 
ment of the particular demonstration that A and b, 
being equal to the same thing c, are equal to each 
other, and of all like cases; nor can it be adduced, 
any more than the Aristotelian maxim, to enforce 
an argument already perfectly conclusive. 

To show the parity of the two cases, we may 
compel the dictum itself to serve as the major pre- 

* That I do not here misrepresent the contracted scope as- 
signed to reasoning by the scholastic logic is shown in the 
following extract from an able little work on the subject by Dr. 
Whately : " Now to remind one, on each occasion, that so and 
so is referable to such and such a class, and that the class which 
happens to be before us comprehends such and such things, — 
this, is precisely all that is ever accomplished by reasoning J* 
— Easy Lessons on Reasoning. The italics are Dr. Whately's. 

f 3 



70 THE THEORY OF REASONING. 

mise of an argument jusfc as easily as we can force 
the mathematical axiom to perform that office, and 
we shall find that, when so impressed into the ser- 
vice, it will be equally inefficient. 

What can be predicated of a class may be 

predicated of any individual of the class ; 
Mortality can be predicated of the class " men;' 7 
Therefore mortality may be predicated of the 
individual man Peter. 

To the conclusiveness of this argument, logicians 
must admit, in accordance with their own doc- 
trine, that the dictum (major premiss, though it 
is) lends no force or cogency whatever. 

But what I have now alleged to show the limited 
sphere of this celebrated maxim is not all. 

So far is the dictum de omni et nullo from having 
any claim to be regarded as the sole principle of 
reasoning, that it cannot be correctly considered 
as the sole principle even of syllogistic reasoning ; 
and this I think is implied in the very doctrines of 
logicians themselves ; for, while they proclaim the 
dictum to be the universal principle, they admit 
that it is not directly applicable to any syllogisms 
but such as can be ranged under the four moods 
of the first figure. 

Now, when it is said that a principle or maxim 
is not applicable, or even not directly applicable, to 
a syllogism, it is equivalent to saying that it can- 
not be educed or drawn from the syllogism, or 



PRINCIPLES OF REASONING. 71 

that the syllogism does not exemplify the maxim, 
or proceed upon it. 

To acknowledge, therefore, that the dictum can- 
not be directly applied to the syllogisms of the 
three other logical figures, is to admit that it is 
not the universal principle even of syllogistic 
reasoning. 

And this is the true state of the case. The dic- 
tum is the principle, or the pair of principles, 
exemplified by syllogisms in the first figure, but 
not by any others. Each figure exemplifies prin- 
ciples of its own, allied to the dictum, but per- 
fectly distinct from it. 

There can be no act of demonstrative reasoning 
from which a self-evident maxim cannot be drawn ; 
and as the kinds of syllogism selected and arranged 
under the figures and moods are all admitted to 
be demonstrative, each kind must be capable of 
yielding its maxim : in other words, from each 
kind a general principle self-evidently true may be 
educed. 

Accordingly we find that the syllogisms in the 
second figure exemplify a pair of maxims allied to 
the dictum, but still distinct from it ; viz. " When 
the whole of a class possess a certain attribute, 
whatever does not possess the attribute does not 
belong to the class," and w when the whole of a 
class is excluded from the possession of an attri- 
bute, whatever possesses the attribute does not 
belong to the class." 

F 4 



72 THE THEORY OF REASONING. 

Analogous maxims may be educed from syl- 
logisms in the third and fourth figures, from each 
of which a single example will probably be thought 
enough. 

The maxim for the moods Darapti and Datisi 
in the third figure is as follows : 

" When the whole of a class possess a certain 
attribute, and the whole or part of the class possess 
another attribute, then some things that possess 
one possess the other." 

And the following is the maxim for the moods 
Bramantip and Dimaris in the fourth figure. 

" When the whole or part of a class possess an 
attribute, and all things which possess that attri- 
bute possess a second, then some which possess the 
second belong to the class." * 

The preceding maxims, except the pair drawn 
from the second figure, which are clear enough, 
are not, it may be allowed, so plain, or so readily 

* When I drew out the above maxims from the second, third, 
and fourth figures, I was not aware that something of the same 
kind had been previously done by Lambert, a German author, 
with whose treatise I am not fortunate enough to be acquainted. 
The reader who wishes to see the maxims as drawn out by 
him, will find them quoted in Mr. Mansel's edition of Aldrich, 
p. 73. and 80. Neither was it present to my mind, that, at a 
much earlier period, the principles of the second and third 
figures had been given in the Port Royal Art of Thinking. 
Had these been before me sooner, I should not have been at the 
trouble of producing mine. As it is, I let the maxims stand in 
their original forms, which differ in detail from those of my 
predecessors. 



PRINCIPLES OF REASONING. 73 

comprehended, as the dictum de omni et nullo ; but 
this arises from the arguments themselves being 
less simple ; whence the several parts of each 
maxim are not so easily kept in view together ; for 
as soon as the terms in which they are expressed 
are understood and their meanings simultaneously 
viewed, they are seen to be self-evidently true. 
Being nevertheless educed from particular argu- 
ments which are equally true and more imme- 
diately evident, they can neither give light nor 
lend force to the syllogisms from which they are 
drawn. In brief, they are altogether useless. 

In these and other respects they are on a level 
with the dictum of Aristotle ; and, although allied 
to that dictum, they are distinct and true in them- 
selves without reference to any thing else. 

The principle that a thing possesses a certain 
attribute when all the class to which it belongs pos- 
sess it, is plainly different from the principle that 
a thing does not belong to a class when it does not 
possess an attribute common to the class. 

Between these two maxims there is as clear a 
distinction as between the axiom that two quan- 
tities are equal to each other when they are re- 
spectively equal to a third quantity, and the maxim 
that two quantities are equal to each other, when 
they are the remainders of two equal quantities 
from each of which the same quantity has been 
taken. They are allied but not identical maxims. 

It results from this examination, that the die- 



74 THE THEORY OF REASONING. 

turn de omni et nullo, is very far from having any 
claim to be considered as the universal principle 
of reasoning ; for, to say nothing of its not being 
the principle of direct contingent reasoning, it has 
been here shown, 

1. That it is only one of the principles of de- 
monstrative reasoning, co-ordinate with many 
others, and 

2. That it is not even the sole principle of 
syllogistic reasoning, but only of those syllo- 
gisms which conform to the first figure. 

Before concluding, it may be useful to advert to 
the importance of distinguishing between such self- 
evident general principles or maxims as have here 
been considered, and those general propositions re- 
garding objects and events which are the results 
of observation : nor is it superfluous after the pre- 
vious explanations to discriminate and contrast 
them. The maxims in question are self-evident ; 
their truth is discerned as soon as they are under- 
stood, and denying them is seen to involve a 
contradiction. On the other hand, a general pro- 
position formed from observing a number of facts, 
although it may be quite convincing, depends for 
that quality on the facts observed, and it may be 
called in question without inconsistence or absur- 
dity. The self-evident maxim cannot be used as a 
proof, because the argument which it might be 
employed to confirm is equally self-evident ; while 
the general proposition obtained from the observa- 



PRINCIPLES OF REASONING. 75 

tion of facts, so far from being an ineffective ge- 
neralisation, either constitutes or represents the 
whole proof of the particular conclusion sought to 
be established. The same remarks will apply, 
mutatis mutandis, to general theorems obtained by 
deduction from incontrovertible premises : having 
been first demonstrated themselves, they subse- 
quently form the real proofs of particular con- 
clusions. 

A brief notice may also be usefully bestowed on 
some observations, in reference to the present sub- 
ject, which appear to have originated in a wrong 
apprehension of what maxims are. 

It has been alleged as an objection by some 
writers, that the dictum^ de omni et nullo is a prin- 
ciple of no great depth, and by others that it is a 
self-evident proposition, little better than a mere 
truism — allegations clearly well founded ; but it 
is not so clear how they are meant to be applied, 
or what they are intended to enforce or to illus- 
trate. 

All the maxims of which acts of demonstrative 
reasoning are exemplifications, must, from the very 
nature of the case, be self-evident propositions, and, 
consequently, may be affirmed to be of no great 
depth. Such acts of reasoning could not be de- 
monstrative, if self-evident maxims were not edu- 
cible from them. To allege this self-evidence as a 
fault or objection, is consequently to mistake the 



76 THE THEOKY OF REASONING. 

position and value of the maxims which it cha- 
racterises. 

In treating the dictum of Aristotle separately, it 
has been impossible to avoid repeating what has 
been already said, and forestalling some explana- 
tions which will find their fitting places in a sub- 
sequent chapter ; but the erroneous light in which 
logicians have continued even down to our own 
times to view this celebrated maxim, seemed to 
call for a particular examination of its true cha- 
racter and position. 



FORMS OF REASONING. 77 



CHAP. VII. 

FORMS OF REASONING, AND ESPECIALLY THE 
SYLLOGISM. 

No doctrine is more clearly and unequivocally 
maintained by logicians, than the sameness, in all 
cases, of the reasoning process, whatever the sub- 
ject-matter of the argument may be. And if the 
dictum de omni et nullo truly represented what, in 
all cases, constitutes reasoning, and were the only 
principle on which, according to common phraseo- 
logy, that operation proceeds, the doctrine would 
be undeniable. 

But, in the first place, if the account already 
given is accurate, there are at least two processes 
of which reasoning is the common name, broadly 
distinguished from each other ; distinct in the na- 
ture of the proofs adduced, distinct in the prin- 
ciples exemplified, and distinct in the state of mind 
resulting. 

In the second place, if we confine our attention 
merely to demonstrative reasoning, and look at the 
general principles on which that species of reason- 
ing proceeds, we find, as shown in the two last 
chapters, that they are numerous ; that the dictum 
de omni et nullo is only one amongst the set ; and, 
if the number of such axioms or principles is to 



78 THE THEORY OE REASONING. 

be the criterion, demonstrative reasoning must be 
pronounced multiplex. If we call it one species of 
reasoning, the varieties under this species must be 
formed by a reference to the general principle of 
which each act of reasoning is an exemplification, 
or, in other words, on which it proceeds. 

Besides the doctrine that reasoning is one and 
the same process in all cases, or as a part or sequel 
of the doctrine, it is further contended, that all 
reasoning may be thrown into the form of three 
propositions ; that every conclusion is really de- 
duced from two other propositions; and that the 
syllogism which contains the three exhibits a 
correct analysis or representation of the one 
identical process.* 

What has been already said in the foregoing 
chapters supplies, in some measure, a refutation 
of the substantial portion of these assertions ; but it 
may be useful to enter into a more minute con- 
sideration of the errors comprised in them. 

With regard to the forms in which reasoning 
may be exhibited, it has been shown, in the two 
last chapters, that what I have ventured to term 
direct contingent reasoning may be expressed in 
two ways, or rather assumes two different forms. 

The type of one is, 

* Thus, in the Port Royal Logic it is said, " No enthymeme 
is conclusive, save in virtue of a proposition understood, which, 
consequently, ought to be in the mind though it be not ex- 
pressed." Part iii. chap. ix. 



FORMS OF REASONING. 79 

All men as far as observation has extended 

have been fallible ; 
Therefore this man [whose fallibility has not 
been matter of observation] is fallible. 
The type of the other is, 

All men as far as observation has extended 

have been fallible ; 
Therefore all men are fallible. 
In reasoning of this description the strict de- 
monstrative syllogism can obviously have no place. 
We may, indeed, vary the first type by in- 
troducing a minor premise, and thus throw the 
argument into three propositions ; but we should, 
in this way, obtain only a quasi-syllogism, not a 
real or demonstrative one. In the case of the 
second type, even this is impracticable, although 
even here we may construct a somewhat different 
quasi-syllogism by generalising the argument into 
" what all men have been all men are," and in- 
troducing the general proposition or maxim so 
created as a major premise ; a procedure which, as 
I have already shown in part, and shall hereafter 
show more fully, is vain and nugatory. 

When, indeed, we have once legitimately in- 
ferred a general law, and employ it as a major 
premise, from which to deduce particular inferences, 
contingent reasoning falls into class-reasoning, and 
becomes in form demonstrative, without however 
acquiring any additional force from its new shape. 
The assertion then above quoted, that all reason- 



80 THE THEORY OF REASONING. 

ing may be thrown into syllogisms is not true of 
direct contingent reasoning. 

We turn then to demonstrative reasoning, and 
inquire whether this is all syllogistic; whether 
every conclusion in demonstrative reasoning is 
really deduced from two other propositions called 
respectively the major and the minor premise; and 
whether consequently the syllogism can be re- 
garded as a true analysis or correct representation 
of the process in every instance. 

When it is affirmed that every conclusion is 
really deduced from two other propositions, the 
assertion, if it means any thing, must mean either 
that when any person draws an inference he has 
two other propositions in his mind, or that two 
other propositions are requisite to make the infer- 
ence valid ; but, for my own part, I find myself 
continually drawing inferences from facts which 
if expressed in language at all may be fully ex- 
pressed in a single proposition, and I am not 
able to discover that such inferences can be ren- 
dered more valid by adding another proposition 
to it. It will not, I think, be difficult to show 
that in two distinct cases, we have in our minds 
only one fact, or one set of facts, expressible in a 
single proposition, on which the inference depends ; 
that, in the one case, there is nothing in the mind 
corresponding to the minor premise of a syllogism, 
and, in the other, nothing corresponding to the 
major premise, and that in both cases the single 
premise suffices for the validity of the conclusion. 



FORMS OF REASONING. 81 

Hence, if there were no other objections to the 
doctrine, the syllogism could not be regarded as a 
correct representation or analysis of every intel- 
lectual process termed reasoning. 

In regard to the first point, it will not require 
much skill to show that what is termed the minor 
premise is so far from being essentially necessary 
to a perfect process of reasoning, that, in certain 
cases, it cannot be forced into the verbal expres- 
sion or representation of that process without 
puerility or supererogation; and when it is thus 
forcibly introduced, it adds no strength to the con- 
clusion, and there is really nothing in the process 
to which it corresponds. 

Let us take a familiar instance before employed. 
A naturalist finds the remains of a horned quad- 
ruped, and pronounces that it was a ruminant 
animal. The reasoning here, if considered as class- 
reasoning, is perfectly expressed by a single pre- 
mise with the conclusion. 

All horned quadrupeds are ruminant ; 

Therefore this horned quadruped was rumi- 
nant. 
A logician may say, " Yes ; but you here com- 
prise in the conclusion two facts or propositions ; 
and, when these are separated, you obtain a regular 
syllogism. 

All horned quadrupeds are ruminant ; 

This quadruped had horns ; 

Therefore it was ruminant." 
G 



82 THE THEORY OF REASONING. 

The introduction of a separate proposition, never- 
theless, is obviously forced ; it adds no strength 
to the inference, and represents no separate mental 
operation. The naturalist sees before him at a 
glance the remains of a horned quadruped ; and 
he believes it to have been ruminant because he 
knows that these attributes have been always 
found conjoined. In relation to the fact before his 
eyes, this knowledge enables him to draw an im- 
mediate inference. You may say that it is a com- 
pound fact, and you may decompose it into the 
two facts of the animal having four legs and having 
two horns ; and then contend that these were 
joined together by a distinct mental act corre- 
sponding to the minor premise. But all this is 
pure invention of what no one is conscious of, as 
will be manifest, if we strip the instance of some 
of its accessories. Suppose the naturalist to find 
only the horns, and to infer that the animal they 
belonged to was ruminant. The whole of what 
passed in his mind would be represented in two 
propositions : " All animals having such horns as 
these are ruminant ; therefore the animal to 
which these horns belonged was ruminant." 

If you attempt to introduce a minor premise, 
you fall into the identical proposition, " The 
animal to which these horns belonged had such 
horns." Or, take the trite argument, that Peter is 
fallible because he is a man, and all men are fallible. 



FORMS OF REASONING.. 83 

The following enthymeme is surely as cogent and 
complete : 

This man is fallible 

Because all men are fallible. 
In order to make this into a syllogism, you must 
again resort to a mere identical proposition. 

All men are fallible ; 

This man is a man ; 

Therefore this man is fallible. 
In what way can such an excrescence as the 
minor premise here lend any force or clearness to 
the inference, or be considered an indispensable 
step ? It seems to me indeed strange, and almost 
ludicrous, to maintain that you cannot draw an 
inference from the visible or notorious qualities of 
an object without a separate mental act, silently 
pronouncing that such qualities do really belong to 
the object ; that, in the example cited, you are not 
capable of concluding the man before you to be 
fallible, until you have passed through the intel- 
lectual operation (if it can be so called) represented 
by the identical proposition " this man is a man ; " 
or until the discovery that his name is Peter has 
relieved you from the awkwardness of exemplifying 
the literal formula a = a. 

It is obvious that the minor premise is needless 
or supererogatory, when the subject of the con- 
clusion manifestly belongs to the class of which 
something is predicated in the major. The sole 
office of the minor, in syllogisms of this form, is to 

G 2 



84 THE THEORY OF REASONING. 

declare the subject of it to be one of the class ; and 
when that circumstance is already as evident as it 
can be, such a declaration is not only superfluous, 
but impertinent. 

It may be remarked, too, that the enthymeme 
above cited fully corresponds to the dictum de omni 
et nullo, " What is predicated of a whole class may 
be predicated of any individual contained under it." 
The universal principle of reasoning, as it has been 
called, forgets the minor premise, and is perfectly 
exemplified by enthymemes which omit it. The 
argument, " Fallibility may be predicated of all 
men ; therefore it may be predicated of this man," 
is a complete exemplification of the dictum. Even 
all class-reasoning, then, is not syllogistic. 

In regard to the second point which I have un- 
dertaken to establish, and which is of much greater 
importance than the other, a brief exposition (only 
repeating, indeed, what has been said before) 
will suffice to show that a perfect piece of reason- 
ing may consist of what is usually called the minor 
premise with the conclusion, and without any 
major premise. This is true of certain cases of 
demonstrative reasoning, as explained in the pre- 
ceding chapter. Take once more the simple 
instance, the lines a and b are equal to each 
other ; for they are severally equal to c. 

Here the reasoning is complete. You may 
indeed form a general proposition, and make it 
into a major premise, as was shown in the chapter 



FOEMS OF SEASONING. 85 

just referred to. You may enunciate, that things 
equal to the same thing are equal to each other ; 
A and b are equal to the same thing c ; therefore 
they are equal to each other. 

This general proposition, however, is psycholo- 
gically an after-thought. It may not enter the 
mind at all ; and, what is most important, it adds 
nothing to the force of the argument. The reasoner 
discerns the truth of the conclusion from the parti- 
cular fact expressed in what is termed the minor 
premise ; and, after so discerning it, may or may 
not proceed to discern that the assertion will hold 
good in all cases. The latter is, as already ex- 
plained, the general principle exemplified by the 
argument, or educed from it, and cannot constitute 
a part of it.* 

The procedure of the mind would, in truth, be 
more accurately represented as follows than in the 
syllogism above cited. 

A and B are respectively equal to c ; 
Therefore they are equal to each other : 
And it is also manifest, that a similar con- 
clusion may be drawn as to the mutual 
equality of all things which are equal to the 
same thing. 

* This point is forcibly urged in the sequel to Sematology 
(p. 112) by Mr. Smart, whose writings abound with acute and 
often just observations on logic, beyond those of most living 
authors. I may be permitted, however, to add that in some of his 
views and modes of representing logical subjects I am not able 
to concur. 

g 3 



86 THE THEORY OF REASONING. 

Thus there is an extensive set of cases of de- 
monstrative reasoning, which do not come under 
the head of class-reasoning, and which find a 
perfect expression in the shape of enthymemes. 
To attempt to force them into the syllogistic form 
is to mistake their character, and the circumstances 
on which their cogency depends. It is surprising 
that geometrical reasoning should ever have been 
considered as altogether syllogistic when fully 
spread out ; for, although all its steps are suscep- 
tible of being thrown into that form, it can be 
done in the case of many of them only by the in- 
troduction of self-evident axioms, of which they 
are perfectly independent for their force, and 
which are consequently a useless appendage. 

I have borrowed my illustration from mathe- 
matical reasoning; but the same superfluous or 
excrescent character of the major premise may be 
observed in certain cases of reasoning on moral 
and physical subjects. Revert, in proof of this, to 
the instances of demonstrative reasoning cited in 
the third chapter. One of them will suffice here 
for illustration : " The planets are opaque bodies ; 
therefore they must shine by light derived from 
an external source." It is obvious that a propo- 
sition affirming that all opaque bodies shine by 
light derived from external sources, would be 
merely generalising an argument sufficiently con- 
clusive, and would not add to it a particle of 
cogency. 



FORMS OF REASONING. 87 

The class of demonstrative inferences before 
pointed out, in which the premise and the conclu- 
sion differ only in presenting the same fact under 
two several aspects, likewise require no major 
proposition ; as, " This man is enslaved by his 
appetites ; therefore he is not free : " where the 
reasoning, which appears puerile enough already, 
would be rendered still more so by prefixing the 
general assertion, " No man who is enslaved by 
his appetites is free." * 

The same may be said of those inferences which 
take place in the conversion of propositions : e. g., 
No man is infallible ; 
Therefore no infallible being is a man. 

In a former chapter I remarked that all in- 
stances of conversion are really instances of de- 
monstrative reasoning, being pure enthymemes 
which require no major premises. That the 
latter may be supplied, and that, when supplied, 
they are perfectly inefficient in adding strength to 
the argument, and therefore wholly superfluous, 
may be easily shown. 

Let us try this experiment on the instance of 
conversion just cited. It may be transformed into 
the following syllogism : 

When a class are excluded from an attribute, 
all beings who possess that attribute are 
excluded from the class ; 

* This is, however, an actual syllogism given in the Elements 
of Logic. 

g 4 



88 THE THEORY OF REASONING. 

The class " men " are excluded from the at- 
tribute of infallibility ; 

Therefore all beings who possess infallibility 
are excluded from the class "men." 
Here it is manifest that nothing is gained but a 
mass of verbiage by the introduction of a major 
premise. The enthymeme is equally cogent, and 
more readily seen to be so. 

To elucidate the subject still further, let us take 
another demonstrative enthymeme : 

The world exhibits marks of design ; 

Therefore it is the work of an intelligent 
author. 
This argument, so expressed, is an example of 
necessary implication as much as if any one were 
to say, " This is a thought, therefore it must have 
proceeded from a thinker." In order to make it 
into a syllogism, we must prefix the general pro- 
position, " Whatever exhibits marks of design 
has had an intelligent author ; " but if any one 
does not discern the conclusion to be implied in 
the minor premise, he will not be convinced by the 
addition of the major, which can lend no force 
to the argument, being merely a generalisation 
of it. 

The instances which I have hitherto adduced, 
all exhibit self-evident implication of one thing by 
another ; but there are cases in which the asserted 
implication is not self-evident, and yet the reason- 



FORMS OF REASONING. 89 

ing can gain no force from its being taken out of 
the form of an enthymeme. 

Suppose any logician to assert that " Solon was 
a wise legislator," and on inquiring into the reason 
of his assertion, he answered, " Because he adapted 
his laws to the genius of the people." If I were 
not satisfied with this reason, and pushed my 
questioning further, " Why do you consider him 
as a wise legislator for doing this ? " he, as a 
logician, might reply, " All legislators who do this 
are wise." Such a reply, nevertheless, would leave 
me just as I was. The reasoning, indeed, would 
be rounded into a perfect syllogism ; the major 
premise would be supplied, and, if admitted at the 
outset, the conclusion must be admitted with it; 
but, starting from the conclusion as a proposition 
to be proved, I should be no more satisfied than I 
was before. If I were not convinced that Solon 
proved himself a wise legislator by adapting his 
laws to the genius of the people, I should not be 
satisfied by the major proposition ; and if I were 
convinced, the major proposition would be need- 
less, for the same reason in both cases, namely, 
that it would be nothing more than a generalisa- 
tion of the particular argument. 

It is not that such reasoning is self-evident, and 
the denial of its validity involves a contradiction ; 
but that to generalise it into a major proposition 
does not add to its force. If you wish to strengthen 
it you must find something different from a major 



90 THE THEORY OF REASONING. 

premise, as, for example, " For when laws are 
adapted to the genius of the people they are cheer- 
fully obeyed." 

In reference to such cases it is to be considered 
that to discern one fact to be implied in another 
requires a certain degree of knowledge. Where 
the subjects of the reasoning are simple, and the 
necessary knowledge is a common possession, the 
implication appears at once self-evident, as in 
geometry, which is concerned exclusively with 
lines and angles. But where the subjects of the 
reasoning are complex, one fact may be really 
implied in another, although the implication is not 
discernible without considerable knowledge and 
study. Whether the implication, however, is im- 
mediately self-evident or not, a general proposition 
in the form of a major premise is alike inoperative 
as a proof. It could be obtained only by general- 
ising the particular argument, and general propo- 
sitions so obtained are wholly inefficient and su- 
pererogatory in establishing the conclusion. When, 
on the other hand, they are obtained by collecting 
facts, or are the result of previous deduction, they 
are, as remarked in the last chapter, essentially 
necessary to the inference. 

If we compare the instances last adduced with a 
syllogism or enthymeme which has for its major or 
only premise either a collective fact respecting a 
class of objects, or a law of nature deduced from 
such a fact, we shall find that, in the latter case 



FORMS OF REASONING. 91 

the force of the argument is wholly dependent on 
the general proposition, or on the collective fact 
from which it has been deduced. 

As an example, the old well-worn syllogism 
before cited will do as well as any other : 
All men are mortal ; 
Peter is a man ; 
Therefore he is mortal. 

Here the allegation that Peter is a man would 
constitute no sufficient ground for concluding him 
to be mortal ; it merely brings him within the 
general fact or law which is the real reason. It 
is the latter that makes the argument good; the 
minor premise would be of non-effect without it. 

But in the case of the enthymemes, and more con- 
spicuously the mathematical demonstration before 
cited, the minor, or rather the only premise, suffices 
of itself, and can borrow no strength, as a reason, 
from the addition of the major; which being a 
mere generalisation of the argument after its co- 
gency must have been seen, would be more properly 
termed a corollary than a premise.* 

To sum up in reverse order what has been said 
of the forms of demonstrative reasoning : — 

* In reference to the same argument, the author of Semato- 
logy observes, "In this instance the axiom which forms the 
major proposition is superfluous : it is not an inductive whole, 
like " Man is mortal," from which we deduce the more parti- 
cular comprehended in it ; but the particular, suppose it to occur 
to the mind for the first time, is as certainly understood to be 
true as if it came after millions of instances." — Sequel to 
Sematology, p. 112. 



92 THE THEORY OF REASONING. 

In arguments where a particular fact implies 
another fact, or, to express it differently, where 
what is usually called the minor premise implies the 
conclusion, a general proposition or major premise 
is redundant ; and such reasoning, so far from being 
syllogistic, cannot even be considered as class- 
reasoning at all, or as in anywise exemplifying 
the dictum de omni et nullo or other allied dicta. 
Of these acts of reasoning the geometrical enthy- 
meme is the best type. 

On the other hand, where the major premise or 
a general proposition implies the conclusion, a 
minor premise is sometimes needful and sometimes 
superfluous : — needful when the subject of the 
conclusion does not manifestly belong to the class 
designated by the middle term or spoken of in the 
major premise ; superfluous when it manifestly 
does. 

All such reasoning, whether with or without a 
minor premise, exemplifies the scholastic dictum 
or other dicta allied to it. 

We are thus brought to the conclusion that in 
numerous cases of demonstrative reasoning, one 
premise is alone sufficient for the inference, although 
it may be granted that, even in those cases, it is 
possible to form a complete syllogism by thrusting 
in a fruitless and redundant proposition. 

It follows, also, from what has been said, that it 
is inappropriate and incorrect to call the syllogism 
an analysis of the process of all demonstrative 



FORMS OF REASONING. 93 

reasoning, and much more so to apply the assertion 
to all reasoning whatever. 

An analysis of reasoning ought to be an account 
of what takes place in the mind when it draws an 
inference, or is determined to a conclusion. Now 
from the preceding representations, it is manifest 
that a single fact or combination of facts, capable 
of being expressed in one proposition, frequently 
determines the mind to a conclusion without re- 
ference to any thing else. This is the whole of 
which the mind is conscious, or which can be dis- 
cerned as having taken place on reflection. 

Supplying in such cases the missing premise, as 
it is called, when it is not introducing a mere 
identical assertion, is simply stating a certain pro- 
position which may be enunciated with truth if 
the argument is valid, but which neither forms nor 
represents any part of the mental process. To 
contend that a second premise is necessary to the 
completion of an argument, because it may by 
some expedient or other always be added to it, is 
like contending that a shawl is an indispensable 
part of a lady's dress because it may always be 
thrown over every thing else in which she may 
be attired. 

This introduction of two premises is in many 
arguments proper and needful, but in some it is 
mere impertinence or supererogation, and in others 
nothing more than the obtrusion of identical 
propositions. 



94 THE THEORY OF REASONING. 



CHAP. VIII. 

PRIMARY OR ORIGINAL PREMISES. 

The preceding chapters have endeavoured to show, 
amongst other things, that what are termed prin- 
ciples of reasoning, or maxims, give no force to 
arguments. They do not constitute real premises 
in any case, and cannot, therefore, be the original 
premises from which we set out. 

What, then, it may be asked, are the primary 
propositions with which our reasonings commence? 

To this inquiry, it may be at once replied, that, 
with the exceptions to be hereafter named, we 
always commence with particular facts ; or, to 
express it more precisely, that particular facts, or 
propositions expressive of them, are, in every case, 
taking into view the whole train of reasoning from 
beginning to end, the first premises from which we 
start, and the ultimate ground at which, in tracing 
back our reasonings, we invariably arrive. 

It has been said, indeed, in contrariety to this, 
that all our reasonings about events, if traced back 
to their origin, will be found to rest on the maxim 
or general principle, as a major premise, that 
similar causes produce similar effects, and that all 
our reasonings in mathematics rest in the same way 
on the several axioms of that science. 



PRIMARY OR ORIGINAL PREMISES. 95 

But, as I have already shown, these general 
principles and axioms are educed from particular 
arguments or instances of implication ; and, if this 
is true, they cannot precede such arguments, nor 
constitute the original premises from which any 
conclusions are inferred. 

Nor can those general propositions which really 
form constituent parts of our reasonings, be the ori- 
ginal premises inquired for. 

Jn contingent reasoning, as already explained, it 
is from particular facts that we form or infer a 
general law ; and, although we may subsequently 
rise the general law as a premise from which to 
deduce particular conclusions, the whole reasoning 
rests on the first facts, and the general law is only 
an intermediate proposition. 

In demonstrative reasoning the same position is 
equally true. At the outset it is always in one or 
more particular facts that we discern another parti- 
cular fact to be implied ; and it is from such par- 
ticular implications that we form those general 
propositions which we use in subsequent deductions. 
From discerning an implication in one instance 
we discern that it must have place in all like in- 
stances. Hence neither axioms, nor general laws 
obtained by contingent reasoning, nor general pro- 
positions employed in demonstrative reasoning, can 
be primary or original premises. 

I am here speaking, on the supposition of the 
whole of a train of reasoning being gone through 



96 THE THEORY OF REASONING. 

by the same mind, or, to state the matter differently, 
I am speaking as if the whole race of thinkers 
constituted one individual. 

Practically we take general propositions or laws 
from various sources without going back to their 
origin — from authority, or testimony, or hypo- 
thesis, — and reason from them without hesitation: 
and if such propositions are furnished to us from a 
source beyond which we cannot ascend, as, for ex- 
ample, by revelation from a superior intelligence, 
they are to mankind original major premises, and 
form exceptions to the doctrine that we always 
commence with particular facts. 

Every man, indeed, is in a position analogous to 
this with regard to general laws on subjects which 
he has not himself investigated, inasmuch as his 
want of knowledge precludes him from ascending 
to the primary facts from which they are inferred. 

Another source of general propositions not ob- 
tained from particular facts, and serving as original 
major premises, is to be found in civil laws, com- 
mands, directions, and rules of conduct generally. 
This is a most extensive source of premises, from 
which we deduce conclusions in practical life ; and 
although it has obviously nothing to do with the 
acquisition of science, the reasoning is precisely on 
a level with that in which the premises are obtained 
by what logicians term complete enumeration, or 
by geometrical inference. 

"If," says Mr. Stewart, " there are any parts of 



PRIMARY OR ORIGINAL PREMISES. 97 

science in which the syllogism can be advantage- 
ously applied, it must be those where our judg- 
ments are formed in consequence of an application 
to particular cases of certain maxims [general 
propositions] which we are not at liberty to dis- 
pute. An example of this occurs in the practice 
of law. Here the particular conclusion must be 
regulated by the general principle, whether right 
or wrong. The case was similar in every branch 
of philosophy, as long as the authority of great 
names prevailed, and the old scholastic maxims 
were allowed, without examination, to pass as in- 
controvertible truths."* 

The doctrine which so long predominated, and 
which still continues to be held by philosophers at 
large, that all our reasonings must be founded on 
general principles or propositions, or, in other 
words, that all our conclusions may be traced back 

* Elements of Philosophy, vol. ii. p. 286. This case of 
general propositions being sometimes given to us, forming an 
exception to the doctrine that the original premises in our 
reasonings are particular facts, has also been well explained by 
Mr. John Mill in his System of Logic, vol. i. 260. Mr. Smart 
expresses the general doctrine of this chapter with clearness 
and precision. After remarking that in tracing back our in- 
ferences we must come at last to something not an inference, 
he continues: "Now this ultimate ground can consist of 
nothing but particular or individual truths, for which we 
have the evidence of our senses or our consciousness." — Prac- 
tical Logic, p. 35. Locke (although the remark is made in a 
different connection) observes that "the immediate object of all 
our reason and knowledge is nothing but particulars." — Essay, 
book iv. chap. 17. 

H 



98 THE THEOKY OF SEASONING, 

to such propositions as primary or original pre- 
mises, has at all times been a formidable obstruction 
to the progress of knowledge. 

We can scarcely suppose that, if men had clearly 
seen the necessity of commencing their deductions 
with particular facts as first premises, they could 
have fallen into those false principles, which, as it 
was, they began by assuming. 



REASONING AND LANGUAGE. 99 



CHAP. IX. 

THE RELATION BETWEEN REASONING AND LANGUAGE. 

As all the acts of reasoning which men communi- 
cate to each other, and even many of those which 
are confined to their own breasts, are put into 
words, language cannot but stand in a very import- 
ant relation to the reasoning process. So intimate, 
indeed, is the connection between them, that many 
logicians have maintained the impossibility of 
reasoning without words. 

Although this is a doctrine which is obviously 
at variance with the whole tenour of the preceding 
views, and virtually refuted by some of the par- 
ticular arguments employed to enforce them, yet, 
from its extensive prevalence, it seems to require a 
distinct examination ; and this examination will 
probably bring out the true relation in which the 
two things before us stand to each other. The 
following is one of the most recent statements of 
the logical doctrine on the subject. 

" Logic is entirely conversant about language," 
or " is wholly concerned in the use of language." 
Accordingly, a syllogism is "an argument so ex- 
pressed, that the conclusiveness of it is manifest 

H 2 



100 THE THEORY OF REASONING. 

from the mere force of the expression, i. e. without 
considering the meaning of the terms." * 

This doctrine, if we take its superficial import, 
seems to narrow the province of logic to only one 
kind of argumentation, by representing it as em- 
bracing only such reasoning as is carried on in 
words. It appears, at first sight, to be founded on 
a distinction between employing language in rea- 
soning, and reasoning without language, and to 
restrict logic to the consideration of the former. 
Unexpressed reasoning, tacit deduction, which 
takes place independently of language, is not, 
arcording to this representation, within the domain 
of the science. 

In this case, it would be necessary either to pass 
over the latter sort of inference altogether, or to 
treat it as something separate and distinct ; but as 
reasoning, whether expressed in language or not, 
is really about things, such a distinction would be 
at the best illusory. 

If the expressions, however, containing the doc- 
trine, are looked at more closely, they will be 
found to imply a much more important proposition, 



* The expressions between quotation marks are the words of 
Dr. Whately in his Elements of Logic, p. 56. 88. 1st ed. 
Dugald Stewart, in his zeal for nominalism, had previously given 
his sanction to the same view : see Elements of Philosophy, 
vol. i. p. 175, 176. 8vo. ed. In a subsequent passage, how- 
ever, Mr. Stewart qualifies the doctrine, as will be hereafter ex- 
plained. 



REASONING AND LANGUAGE. 101 

viz., that there is no reasoning except in words. 
They virtually declare the process to be impossible 
without language, and, moreover, to be so much 
an affair of mere words, that we can reason without 
attaching any meaning to the terms employed. 

Let us examine these two extraordinary po- 
sitions. 

That the various operations of the mind are 
concerned with facts or things, has been already 
shown ; and it is plain that we may think of facts 
and things — we may recollect, conceive, or imagine 
them, without the intervention of signs. Nor is 
language more necessary to the mental act called 
reasoning # , than it is to the operations called 
memory, conception, and imagination. All the 
help which it affords, in this process, is enabling 
the mind to recall and keep in view the facts repre- 
sented by the signs employed. 

The possibility of reasoning in geometry without 
words, cannot, I think, be doubted by any one 
who attends to the movements of his own mind. 

* Even Hobbes, who has been styled plusquam nomi?ialis, 
and who seems, in many passages of his writings, to regard 
reasoning, like truth, as an affair of mere words, now and then 
admits that we may carry on the process without them. He 
says, " Quomodo autem animo sine verbis tacita cogitatione 
ratiocinando addere et subtrahere solemus uno aut altero ex- 
emplo ostendendum est." "But how by the ratiocination of 
our mind we add and subtract in our silent thoughts, without the 
use of words, it will be necessary for me to make intelligible by 
an example or two." — Logic, chap. i. § 2. See also Leviathan, 
chap. v. 

H 3 



102 THE THEORY OF REASONING. 

In tracing the proofs that the three angles of a 
triangle are equal to two right angles, I can, for 
my own part, easily follow the steps of the demon- 
stration without thinking about the language. I 
am led to discern intuitively the equality of cer- 
tain angles to other angles, until I arrive at the 
conclusion ; a discernment which has not the 
slightest concern with words, as I can go through 
the whole deduction without even attaching names 
or letters to the angles.* 

So in contingent reasoning, or drawing conclu- 
sions about events. A great part of our reasoning 
consists in inferring the future from the past, the 
absent from the present, the unknown past from 
the known past. In all these cases what we think 
about are facts. We represent to ourselves the 
objects and events of which we have had knowledge 
or experience, and the future events which, from a 
review of these, we think will happen, or the un- 
observed past events, which we conclude have 
happened. Language may mingle in these opera- 
tions, but it is neither essential to them nor forms 
their principal feature : it may mix itself with our 



* Hobbes acknowledges the possibility of this : he says a man 
that hath no use of speech at all, such as is born and remains 
perfectly deaf and dumb, if he set before his eyes a triangle, 
and by it two right angles, such as are the corners of a square 
figure, he may, by meditation, compare and find that the three 
angles of that triangle are equal to those two right angles that 
stand by it." — Leviathan, part i. chap. iv. 



REASONING AND LANGUAGE. 103 

reasonings, as it does with our recollections and 
imaginings, without at all affecting their substan- 
tial character.* 

It is, indeed, an extraordinary mistake to sup- 
pose that we reason only when we clothe our 
thoughts in words, or deduce our conclusions in 
verbal propositions. It surely requires little re- 
flection to be aware that we every day make a 
thousand inferences with the rapidity of lightning, 
without the possibility of the intermediation of 
language. So far, indeed, are we from being 
obliged to reason in words, that I will venture to 
appeal to the consciousness of the reader whether 
we do not oftener reason without them. While 
performing our commonest actions we are per- 
petually making inferences, and cannot avoid it. 
In taking a walk, for instance, in choosing this 
road, in avoiding that obstacle, in mounting a 
style, or in opening a gate, we are constantly con- 
cluding beforehand what results will follow certain 
acts, without putting these anticipations into lan- 
guage. What rapid inferences are drawn by a 
popular orator who is making a speech to a way- 
ward assembly, and has to adapt his matter and 
his expressions, as he proceeds, to the state of 

* " To suppose," says Dr. Brown, et that we cannot reason 
without language, seems to me, indeed, almost to involve the 
same inconsistency, as to say, that man is incapable of moving 
his limbs till he have previously walked a mile." — Lectures on 
the Human Mind, vol. ii. p. 527. 

h 4 



104 THE THEORY OF REASONING. 

feeling which manifests itself to his observation ! 
He shuns one topic which he intended to introduce 
because he becomes aware that it Yvdll be ill-re- 
ceived; and he introduces another not premedi- 
tated, because his tact enables him to foresee that 
it will make a favourable impression. And this 
instance is the more remarkable as an illustration 
of the view here taken, because a double process 
of reasoning is at one and the same time taking 
place in the mind, The orator not only reasons 
in words to his audience, but is conscious of a 
rapid series of tacit inferences going on within 
him as to what topics it will be proper to avoid 
or profitable to touch upon as he proceeds. 

In some passages of his writings Dugald Stewart, 
quitting for a while the pure logical doctrine, takes 
a view of the subject similar to that here given. 
u We can employ," he says in one place, " the 
agency of air to increase the heat of a furnace ; the 
furnace to render iron malleable ; and \ive can 
apply] the iron to all the various purposes of the 
mechanical arts. Now it appears to me that all 
this may be conceived and done without the aid 
of language ; and yet, assuredly, to discover a series 
of means subservient to a particular end, or, in 
other words, an effort of mechanical invention, 
implies, according to the common doctrines of 
philosophers, the exercise of our reasoning powers. 
In this sense, therefore, of the word reasoning, I 
am inclined to think that it is not essentially con- 



REASONING AND LANGUAGE. 105 

nected with the faculty of generalisation, nor with 
the use of signs." * 

But Mr. Stewart, it must be observed, terms all 
this particular reasoning. He allows, with Hobbes, 
that particular reasoning may take place without 
words ; but general reasoning, he affirms (and 
here he again falls in with the logical doctrine), 
cannot take place except in words. 

He goes even to the extreme nominalism of 
asserting, that without the use of signs all our 
thoughts must have related to individuals, for- 
getting that since a sign must signify something, 
if we could think only of individuals, signs of 
individuals would be the only signs that could 
be invented. Discerning or thinking of a class, 
i. e. a number of individuals resembling each other 
in one or more respects, must precede the act of 
naming a class, otherwise we should be giving a 
name to nothing. 

The example which Mr. Stewart himself adduces 
is sufficient to show the error of his doctrine. 

If a man reasons without language when he 
employs the agency of air to increase the heat of 
a furnace, which he may do, although completely 
deaf and dumb, he has already generalised. When 
he has sent one blast of air into his fire, he sends 
another after it, in the full assurance that he can 

* Elements of the Philosophy of the Human Mind, vol. i. 
p. 207. 8vo. ed. 



106 THE THEORY OF REASONING. 

produce the same effect whenever he chooses ; and 
he infers, with as little doubt, that his neighbour, 
who is building another furnace, will find currents 
of air equally efficient.* 

If this is not generalising and general reasoning, 
what is ? It may possibly be alleged, however, 
although incorrectly, that what I have hitherto 
advanced cannot be applied to syllogistic reasoning. 
Let us consider, then, a case expressly of this de- 
scription. Let us suppose our deaf and dumb 
man to be something of a botanist, and to be 
taking a country walk. He comes to a bank on 
which are growing a number of primroses, and, on 
examining the flowers, he perceives, as he has 
always perceived in similar examinations, that 
each flower contains five filaments or stamens. 
He proceeds in his walk, and sees another prim- 

* Condillac has been classed amongst those who have con- 
sidered language as indispensable to reasoning; and he un- 
doubtedly asserts that the art of reasoning resolves itself into a 
well constructed language. " L'art de raisonner se reduit a une 
langue bien faite," or "a l'art de bien parler." — La Logique, 
partie ii. chap. v. And in another part of the same treatise, he 
tells us, " que les mots nous sont absolument necessaires pour 
nous faire des idees de toutes especes ; et nous verrons bientot 
que les idees abstraites et generates ne sont que des denomina- 
tions. Tout confirmera done que nous ne pensons quavec le 
secours des mots." — Partie ii. chap. v. The last doctrine 
goes even beyond that of Mr. Stewart. There are however, 
other passages in the same treatise not easy to reconcile with 
those I have quoted (see partie i. chap. vii. and partie ii. 
chap, i.) ; so difficult is it to be consistent in error. 



KEASONING AND LANGUAGE. 107 

rose growing on an inaccessible ledge, half-way 
down a perpendicular rock, and " not to be come 
at by the willing hand." Although inspection of 
the flower is precluded, reasoning about it is not, 
and he immediately infers that it has five stamens 
in its corolla, like all which he has examined. In 
this case he would think and infer, without the 
slightest aid from language, just what a syllogism 
expresses. Surely the power of attaching the 
generic name of primrose to the flower could not 
possibly make it a clearer act of reasoning. 

We have next to consider the assertion, that the 
conclusiveness of an argument may be manifest 
from the mere force of the expression, without 
considering the meaning of its terms. 

To employ language in reasoning, without at- 
taching some meaning to the signs employed, 
seems to me, I confess, a sheer impossibility ; and 
there is, to my understanding, a marvellous incon- 
sistency in saying, that the conclusiveness of an 
argument may be manifest from the mere force of 
the expression, without considering the meaning of 
the terms. Expression can have no force but from 
its meaning. Language, in so far as it has no 
meaning, has no strength : it is a mere noise, a 
nullity. 

The writers who thus maintain that the con- 
clusiveness of a properly expressed argument is 
manifest without considering the meaning of the 
terms, exemplify their doctrine as follows : — "In 



108 THE THEORY OF REASONING. 

this syllogism y is x, z is y, therefore z is x, the 
conclusion is inevitable, whatever terms x y z re- 
spectively are understood to stand for." Here is 
an admission, at all events, that they must stand 
for something ; and it is precisely what they stand 
for that constitutes their meaning, and that gives 
force and even intelligibility to the argument. If 
the letters are to be considered as mere letters 
without representative power or symbolical signi- 
ficance, each proposition of the syllogism is false. 
The letter y is not the letter x, nor is the letter z 
the letter y. We must, then, of necessity, consider 
the representative meaning, y must be taken to 
designate some thing or things, and not to stand 
as a mere letter ; x must be taken to designate 
some attribute of y ; and z must be taken as 
meaning y, or as a particular name for a thing also 
called y. The conclusion asserts that z must there- 
fore ha ye the attribute belonging to the thing or 
things called y. 

Here, then, it is manifest, that the meaning is 
everything to the argument. The letters are 
merely helps. 

That a variety of things and attributes may be 
attached to the symbols x, y, z, without altering 
the force of the argument, is a circumstance be- 
longing to the nature of general language. An 
analogous fact in arithmetic is familiar to every 
one. Twice ten are equal to twenty, whether the 
subject of the calculation happens to be shillings 



REASONING AND LANGUAGE. 109 

or pounds, or men or marbles ; but it cannot be 
affirmed, that, on this account, the words twice ten 
are twenty are destitute of meaning, or that their 
meaning is left out of consideration. 

The whole truth of the matter in question (and 
this may have been all which the passage under 
review, so incautiously worded, was intended to 
express) is, that we may reason with terms, how- 
ever general may be their signification, under the 
condition, of course, that they have some significa- 
tion to reason about. * 

It is worth while, in further elucidation of the 
subject, to quote the following paradox, as Mr. 
Hallam justly terms it, thrown out by Hobbes in 
his correspondence with Descartes, for the sake of 
the reply given by the latter, coinciding so exactly 
as it does with the views advanced in the present 
treatise. 

* Mr. E. E. Scott, in his able work entitled " Elements of 
Intellectual Philosophy," gives some acute comments on the 
passage already referred to in Dugald Stewart's first volume, in 
which that philosopher asserts that, in order to perceive the 
justness of the inference (in a syllogism like that quoted above) 
it is not necessary to understand its meaning. " Though I by 
no means admit," says Mr. Scott, " that it is not necessary to 
understand the meaning of a syllogism in order to perceive the 
justness of its inference, yet, without doubt, our assent will be 
given to a syllogism, although its terms be successively varied, 
according to a certain principle." He afterwards adds that a 
syllogism " whose minor is z is an x will never enforce our 
assent, unless we settle, by previous definition, that x denotes 
a genus or species of which z is an individual." p. 1 50. 



110 THE THEOEY OF REASONING. 

" Que dirons-nous, maintenant," writes Hobbes, 
"si peut-etre le raisonnement n'est rien autre 
chose qu'un assemblage et un enchainement de 
noms par ce mot est ? D'ou il s'ensuivroit que par 
la raison nous ne concluons rien de tout touchant 
la nature des choses, mais seulement touchant leurs 
appellations, c'est-a-dire que par elle nous voyons 
simplement si nous assemblons bien ou mal les 
noms des choses, selon les conventions que nous 
avons faites a notre fantaisie touchant leurs signi- 
fications." 

To this curious passage Descartes very aptly 
replied: — 

" L'assemblage qui se fait dans le raisonnement 
n'est pas celui des noms, mais bien celui des choses 
signifiees par les noms ; et je m'etonne que le con- 
traire puisse venir en 1' esprit de personne."* 

In reasoning on some subjects, little progress, 
indeed, could be made without language. It is not 
always seen, however, that this observation is ap- 
plicable far more to written than to spoken lan- 
guage, to visible symbols than to articulate sounds. 
Yet no one would dream of attempting on this 
account to restrict logic to written language. 

The great expedients which have been devised to 
assist the intellect in the most abstract calculations, 



* Quoted from the works of Descartes by Mr. Hallam in his 
Introduction to the Literature of Europe, vol. iii. p. 248. 



REASONING AND LANGUAGE. Ill 

owe their efficiency to their symbols being pre- 
sentable to the eye at pleasure, and thus consti- 
tuting visible fixed stations, where the mind can 
repose, where it can always find what has been 
already accomplished, and from which it can again 
start in pursuit of new results. Sounds, it is true, 
are associated with these visible symbols ; but they 
play a subordinate part in such processes, and 
would be incapable alone of enabling the mind to 
proceed beyond a comparatively short distance. 

Reasoning, in brief, is one species of thinking ; 
and, like all other thinking, except that of which 
language is itself the subject, may be carried on 
independently of words. When language is used, 
it forms only an instrument of the process ; some- 
times, indeed, exceedingly useful, and even indis- 
pensable, but never constituting the process itself, 
any more than laughter constitutes mirth, or a 
frown displeasure ; or, to pass over to another 
class of illustrations, any more than shoes or 
sandals constitute walking, although they may 
help the walker ; or than lenses constitute seeing, 
although without them we could not attain the 
sight of myriads of stars, which, to the unassisted 
eye, are hid in the depths of space. 

The calculus which enabled Adams and Leverier 
to point out the spot in the heavens where an un- 
known planet was wheeling through its remote 
orbit, and the telescope through which Galle dis- 



1.12 THE THEORY OF REASONING. 

covered it*, are both alike instruments by whose 
aid the natural faculties can reach to knowledge 
otherwise inaccessible, but which confer no new 
faculty on the intelligent agent who employs them. 

* It is generally understood that M. Galle of Berlin dis- 
covered the planet Neptune, Sept. 23. 1846, in consequence of 
a communication from M. Leverier. 



SEASONING AND INDUCTION. 113 



CHAP. X. 

THE RELATION OF OBSERVATION, EXPERIMENT, AND 
INDUCTION, TO REASONING AND TO EACH OTHER. 

The terms at the head of the present chapter denote 
closely allied and frequently intermingled opera- 
tions, which it seems desirable to investigate, in 
order to show in what relation they stand to each 
other, and more particularly in what relation 
reasoning stands to the rest. 

Experiment is usually placed in antithesis to 
observation, as if one excluded the other ; but 
surely the intellectual act termed observation is 
just as much required for experiments as it is for 
spontaneous events. Unless experiments are ob- 
served, they can clearly be of no use. It is equally 
true, if not equally clear, that the observation of 
either spontaneous or experimental phenomena can 
scarcely take place without reasoning, and, if it 
could, would be of no scientific value. 

To illustrate this by an example. We observe a 
stone fall rapidly to the ground, and a feather? 
floating in the atmosphere, slowly descend. Me- 
ditating on these events, we conjecture, or infer, 
that the air through which they fall has something 
to do with the difference in the rates of their 
descent. We, in consequence, devise the experi- 

i 



114 THE THEOEY OF REASONING. 

merit (in which, also, reasoning is needful) of 
placing the two substances in a vessel exhausted 
of air ; and we find that, on precipitating them 
from the same height, they come to the bottom of 
the vessel at the same moment. We try other 
substances with a similar result, and finally deduce 
the general law, that all substances at the surface 
of the earth descend in vacuo from equal heights in 
equal times. 

There is evidently here, in the first place, ob- 
servation of facts spontaneously occurring; then 
reasoning or conjecturing something from those 
facts, viz., what would result from withdraw- 
ing the element of air ; further reasoning as to the 
mode of withdrawing it ; acting on this reasoning 
by trying the experiment ; subsequently making 
other experiments ; and finally deducing a general 
conclusion, or law. 

But, not only have we here observation of spon- 
taneous and experimental phenomena with an in- 
termixture of reasoning, but we have in those 
combined operations an example of what is usually 
termed induction. Induction is not some process 
superadded to those here described ; but it is, in 
this instance, a combination of the two intellectual 
operations of observing and inferring, with the 
mechanical aid of experimental contrivances to 
enlarge their range, and for the purpose of de- 
ducing a general law. 

It thus appears, that, instead of contrasting ob- 



REASONING AND INDUCTION. 115 

servation and experiment, we should contrast spon- 
taneous and experimental phenomena as alike sub- 
jects of observation. Facts furnished by artificial 
contrivances require to be observed just in the 
same way as those which are presented by nature 
without our interference ; and yet philosophers 
are nearly unanimous in confining observation to 
the latter phenomena, and speaking of it as of 
something which ceases where experiment begins ; 
while, in simple truth, the business of experiment 
is to extend the sphere of observation, and not 
to take up a subject where observation lays it 
down. 

In regard to Induction, the view which I have 
here taken of it coincides, if I mistake not, with 
that which is to be found in the writings of our 
most eminent philosophers, from Lord Bacon to 
Dr. Brown. 

By logical writers, it has, indeed, been used in a 
much more limited sense, viz., that of inferring a 
general conclusion from either a complete or an 
imperfect enumeration of particular instances*; 

* Thus Le Grand : " Inductio est argumentatio qua ex 
plurium singularium recensione, aliquid universale conclu- 
ditur." — Institutio Philosophise, p. 57, ed. 3. a.d. 1675. And 
Wallis : " Inductio est argumentations seu syllogismi forma, 
qua probatur quid verum esse de generali quopiam, ex eo quod 
verum sit de particularibus omnibus sub eo generali contentis ; 
saltern de tot liorum enumeratis, ut credibile sit de reliquis 
item esse verum." — Institutio Logicce, ed. 4, p. 198. 

i 2 



116 THE THEORY OF REASONING. 

and even some philosophical writers of the school 
of Bacon have employed it, in an analogous ac- 
ceptation, to denote merely the process of inferring 
a conclusion more general than the premises from 
which it is drawn. 

If we turn, however, to the pages of such writers 
as Reid, Stewart, and the more metaphysical fol- 
lowers of Bacon, we shall find the term there sig- 
nifying the process of obtaining or preparing the 
premises, and frequently distinguished from that 
of inferring the conclusion ; in other words, it is 
used to denote that combination of observation and 
reasoning which has been already described as pre- 
ceding the final inference. 

Mr. Stewart, for instance, speaks of " those general 
conclusions concerning the established order of the 
universe, to which, when legitimately inferred from 
an induction sufficiently extensive, philosophers have 
metaphorically applied the title of Laws of Nature;"* 
where the term induction clearly denotes something 
that precedes the inference, and of course does not 
include it. 

In a similar way Dr. Brown speaks of " a wide 
induction." 

" There is a constant tendency," he says, a in the 
mind to convert a general law into a universal law, 
— to suppose, after a wide induction, that what is 
true of many substances that have a very striking 

* Elements, vol. ii. p. 224, ed. 2. 



REASONING AND INDUCTION. 117 

analogy, is as certainly true of all that have this 
striking analogy."* 

Professor Playfair, in giving an account of 
Bacon's method, teaches that we are to begin by 
excluding certain things from our collection of 
facts. "This exclusion," he continues, "is the 
first part of the process of induction."! 

Other writers speak of "a partial " and " an in- 
complete " induction, phrases manifestly referring 
to the observation or examination of instances. 

In the preceding passages induction is clearly 
regarded as a process of investigation preparatory 
to the formation of a general law. 

This process may be more or less complicated 
according to circumstances, and includes or may 
include, as I have shown, observation of both 
spontaneous and experimental phenomena, and the 
intermixture of such inferences as may be necessary 
to establish what I have before termed the collective 
fact, from which the general law is to be deduced. 

It must be allowed, nevertheless, that there is a 
good deal of laxity in the employment of the word, 
even in the writings of our most eminent philo- 
sophers. Lord Bacon manifestly uses it to denote 
a mixed process of observation and reasoning ; but 
he is not altogether exempt from the common want 



* Lectures, vol. i. p. 191. 

f Preliminary Dissertations. Encyclop. Britannica, p. 460. 



118 THE THEORY OF KEASONING. 

of precision in applying it*, and he sometimes in- 
cludes, under the term, the formation or deduction 
of the general law as well as the examination of 
instances. Newton has, I think, fallen into an 
ambiguous use of the word in a passage which 
occurs at the conclusion of his " Optics." While the 
extract now presented will furnish an instance in 
point, it will exemplify also the manner in which 
observation and experiment are commonly, and in 
my view inaccurately, distinguished. 

" Analysis [in natural philosophy] consists in 
making experiments and observations, and in 
drawing conclusions from them by induction, and 
admitting of no objections against the conclusions 
but such as are taken from experiments or other 
certain truths. For hypotheses are not to be 
regarded in experimental philosophy. And al- 
though the arguing from experiments and obser- 
vations by induction be no demonstration of general 
conclusions ; yet it is the best way of arguing which 
the nature of things admits of, and may be looked 
upon as so much the stronger by how much the 

* " Inductio enim quae procedit per enumerationem simplicem 
res puerilis est, et precario concludit, et periculo exponitur ab 
instantia contradictoria et plerumque secundum pauciora quam 
par est, at ex his tantummodo quae praesto sunt pronunciat. 
At inductio, quae ad inventionem et demonstrationem scien- 
tiarum et artium erit utilis, naturam separare debet per 
rejectiones et exclusiones debitas, ac deinde, post negativas tot 
quot sufficiunt, super affirmativas concludere." — Nov. Org., 
lib. i. aph. cv. 



REASONING AND INDUCTION. 119 

induction is more general: and if no exception 
occur from phenomena, the conclusion may be 
general."* 

In the first and second use of the term in this 
passage, the intention of the writer was manifestly 
to characterise the drawing of the conclusion, al- 
though the meaning is not very happily brought 
out, since we cannot with propriety speak of draw- 
ing conclusions by means of the operation itself, or 
of any other operation. In the last use of the term, 
he evidently meant to characterise the comprehen- 
siveness of the preliminary observation. 

I have already cited Mr. Stewart as using the 
term induction, to denote the course of investigation 
preparatory to the formation of a general law ; but 
in another passage, where he describes the method 
of induction, he includes also the final inference. 

" Wherever," he says, " an interesting change is 
preceded by a combination of different circum- 
stances, it is of importance to vary our experiments 
in such a manner &s to distinguish what is essential 
from what is accessory ; and when we have carried 
the decomposition as far as we can, we are entitled 
to consider this simplest combination of indispen- 
sable conditions as the physical cause of the event. 

" When by thus comparing a number of cases, 

* Dr. Johnson gives the greater part of this passage in his 
Dictionary, to support his second definition of the term, bor- 
rowed from Watts's Logic, viz- " Induction is when from 
several particular propositions we infer one general." 

i 4 



120 THE THEORY OF REASONING. 

agreeing in some circumstances, but differing in 
others, and all attended with the same result, a 
philosopher connects, as a general law of nature, the 
event with its physical cause, he is said to proceed 
according to the method of induction. This, at least, 
appears to me to be the idea which, in general, 
Bacon himself annexes to the phrase ; although I 
will not venture to affirm that he has always em- 
ployed it with uniform precision. I acknowledge 
also that it is often used by very accurate writers, 
to denote the whole of that system of rules of which 
the process just mentioned forms the most essential 
and characteristical part." * 

It appears then, from the authorities I have cited, 
that there are at least three different modes of em- 
ploying the term ; viz. to denote, 

1. The investigation of facts, preparatory to the 
formation of a general law ; 

2. The mere inferring of the general law from the 
facts brought together by such investigation ; 

3. The two preceding processes combined. 

The first of these acceptations appears to me to 
be the most conformable to the general usage of 
philosophical writers, and for that reason the most 
convenient to adopt. 

If this discussion should appear to turn on a mere 
question of phraseology, it must still be allowed, 
that to settle the meaning of so important a word 

* Elements, vol. ii. p. 348. 



EEASONING AND INDUCTION. 121 

as Induction is exceedingly desirable and worth 
some pains. At present it may be doubted whether 
any two men of science, taken at random and not 
being technical logicians, would give the same de- 
finition of it. 

My principal aim, however, in the present chapter 
has been, in consonance with the subject of my 
treatise, to point out how far reasoning is concerned 
in this important combination of intellectual oper- 
ations. I have accordingly endeavoured to show, 
that induction cannot be carried on without a con- 
tinual intermixture of inferences with observation ; 
and that the result to which the whole converges, 
is the formation of a general law, — itself an act of 
contingent reasoning. 



122 THE THEORY OF REASONING. 



CHAR XL 

RULES FOR GUIDING THE OPERATIONS OF REASONING, 
AND ESPECIALLY THE RULES OF THE SCHOLASTIC 
LOGIC. 

A true theory of the reasoning processes, or, in 
other words, a thorough comprehension of their 
character, although fortunately not essential to the 
right performance of the acts, may be expected to 
assist us in some degree to arrive at correct con- 
clusions ; but will perhaps be more especially 
serviceable in preventing that misdirection of our 
powers, and that waste of attention on wrong ob- 
jects, which are the usual results of a false theory 
on an important subject. 

It must also tend to inspire us with confidence 
in our deductions, and with fearlessness in sub- 
mitting them to the examination of others, in pro- 
portion as it enables us to discern the character of 
every link in the chain of argumentation. 

Whether, nevertheless, such an insight into 
the nature of the processes will afford any formal 
rules to guide us in the performance of them, and 
whether any such rules are needed, seem to be 
points not equally clear. 

From the preceding exposition of the subject, it 



RULES IN REASONING. 123 

will have been seen, that the operations which pass 
under the name of reasoning are of a simple cha- 
racter ; so simple, indeed, that a thorough compre- 
hension of what they are seems all that is requisite 
to guard us against any irregularity to which they 
may be liable, if they are liable to any. 

But this is a question which will perhaps be best 
elucidated by a separate examination of it in rela- 
tion to each species of reasoning. 

Section I. 
Rules in Contingent Reasoning. 

In regard to those acts of contingent reasoning 
from one individual event to another, which are 
constantly occurring in the common business of 
life, rules can scarcely have place, since in them 
we do nothing but infer that some unknown event 
will happen, or has happened, in certain circum- 
stances, from our having known a similar event to 
have taken place in similar circumstances : if any 
precept is wanted to guard us from mistakes, it is 
merely an injunction to take care that our pre- 
mises are correct, i.e. that the circumstances are 
similar. We may erroneously regard cases as 
resembling each other, which really do not ; a 
fault of observation, or a misconception, or a mis- 
recollection, rather than an error of inference. 

When, however, we turn to those important acts 
of contingent reasoning which consist in the in- 



124 THE THEORY OF REASONING. 

ference of general laws, the case is somewhat 
altered in its aspect, and the operation seems less 
simple. Yet still it will be found, if I mistake 
not, that the greater complexity which then ap- 
pears is the complexity of the several operations 
concerned in the preliminary inquiry needful to 
collect and arrange the facts from which the in- 
ference is to be drawn. 

Accordingly, if we examine the rules which 
have been laid down by Lord Bacon and his fol- 
lowers, we shall find that they are precepts for 
carrying on induction (in the sense annexed to 
that term in a former chapter) ; for instituting 
experiments, altering the combination of circum- 
stances by leaving out some or adding others, and 
watching the results ; which operations are not 
reasoning, although reasoning, as before explained, 
must be, or may be, employed in conducting them. 

They are to be regarded, in truth, as engaged in 
establishing the collective fact, or the premises 
from which inferences to new cases are to be 
drawn, or a general law is to be inferred. 

When it is stated, for example, from an ample 
survey of the subject, that a certain cause has 
always, as far as observation has extended, pro- 
duced a certain effect, this is not an inference or 
conclusion, but simply giving the summary result 
of inductive investigation. 

When, however, we expect or predict, on a new 
occurrence of the cause, that the effect will follow, 



EULES IN REASONING. 125 

or lay down the general law that the cause always 
produces the effect, we do not state a mere matter 
of fact, but we draw an inference ; it is, in either 
case, an act of direct contingent reasoning. 

Thus, in the formation of a general law, as in 
the inference of one particular event from another, 
the operation which is solely entitled to the appel- 
lation of reasoning is equally simple ; and the 
question is, can so simple a process go wrong, and 
the correct performance of it be assisted by rules ? 

It is undoubted that we constantly witness in- 
stances of hasty and undue generalisation, or, in 
other words, of drawing general inferences not 
warranted by the facts from which they are drawn ; 
and these seem, after the strictest analysis, to be, 
on many occasions at least, really errors of rea- 
soning. 

When a person, smarting under the dishonesty 
of some pretended friend, who has betrayed him 
for a bribe, exclaims, " Every man has his price," 
he draws his universal inference from a single case, 
and it is immediately seen by others to be a hasty 
and undue generalisation. This example, indeed, 
we may consider in two lights. If we regard the 
conclusion, it is obviously too wide for the premise; 
if we regard the premise, it is obviously too scanty 
for the conclusion ; but in whatever light we 
regard the argument, the mistake is in drawing 
the inference, not in laying down the premise. 
The fact forming the premise, viz., that a friend 



126 THE THEOEY OF REASONING. 

has been seduced from his duty by a bribe, is the 
only fact (by hypothesis) before the reasoner ; and 
if he draw an inference from it at all, it should be 
one of something like corresponding extent, as, 
" therefore, other men in similar circumstances 
may be occasionally expected to act in the same 
way." To deduce a universal conclusion in such a 
case from a single fact is manifestly an error of 
deduction. 

The error, however, of many of these instances 
of unwarranted generalisation lies in the premises. 
A part only of the facts have been properly ex- 
amined, and yet the whole are assumed to have 
been so. The premises in these cases, as expressed 
or asserted, warrant the inference, and the erro- 
neous conclusion is, therefore, due to the manner 
in which they are assumed. Undue generalisation 
results probably oftener from this cause than the 
other, and is to be corrected by nothing but stricter 
attention to facts. 

Even in cases where, as in the example above 
cited, the fallacy is evidently in the reasoning, an 
instructive method of attempting to correct it 
would be trying how far other facts would bear 
out the conclusion ; endeavouring, in a word, to 
enlarge the premises, rather than to shape the 
conclusion to the dimensions of the single fact, 
although the last method of proceeding has also its 
value. 

These considerations show that rules for avoiding 



RULES IN REASONING. 127 

erroneous conclusions in contingent reasoning are 
in the main rules for the investigation of facts, or 
for laying down premises, and belong to the general 
art of inductive inquiry. 

Perhaps the only rule of practical importance to 
guard us against pure errors of inference in these 
cases (expressed in general terms), is the injunction 
to proportion the extent or generality of the con- 
clusion to the facts from which we draw it. When 
these facts are susceptible of numerical expression, 
the law which we can deduce from them becomes 
susceptible of the same. The methods of calcu- 
lation, in such cases, come under a separate science, 
usually termed the Theory of Probabilities, which 
is itself an auxiliary of induction, and may be 
regarded as an offset or branch of contingent 
reasoning. The result of it, when its methods are 
well applied, is to proportion, with all possible 
exactness, the law deduced to the facts from which 
it is inferred. 

Section II. 

Rules in demonstrative Reasoning, and especially 
in Class-Reasoning. 

We have next to inquire how far demonstrative 
reasoning may be assisted by rules. 

In that branch of it which is not class-reasoning, 
and of which the mathematical enthymeme may be 
regarded as the type, there seems to be no place 



128 THE THEORY OF REASONING. 

for rules to guide the process or guard it from 
error. That one thing is implied by another is 
discerned at once ; or, if not, it can be discerned 
only by acquiring the necessary knowledge to 
discern it. 

We cannot, however, so easily dismiss that va- 
riety of demonstrative reasoning which is usually 
termed syllogistic, but which, for reasons before 
assigned, I have denominated class-reasoning, 
although it is really as simple as the rest, and 
requires, like them, little or no assistance from 
rules. But learned men long thought, and many 
of them still continue to think, otherwise. It is 
one of the remarkable circumstances in the in- 
tellectual history of the world, that between two 
and three thousand years ago, this simple process 
of class-reasoning was regarded as a matter of 
such great nicety and difficulty, that a compli- 
cated system of rules was expressly devised to 
prevent mistakes in performing it. In subsequent 
ages of unsound philosophy, the scholastic logic 
became still further exalted and magnified to an 
undue and even preposterous importance. The 
very narrowness of its range appears to have con- 
centrated the skill and ingenuity of the human 
mind on the contrivance of an intricate machinery 
to accomplish the little there was to do in this 
limited sphere, under the impression that it was 
much, and that it was absolutely all. 

That species, or rather that variety of reasoning, 



RULES IN REASONING. 129 

which consists in predicating an attribute of some 
individual or individuals of a class, because it 
is predicable of all the class, or in other allied 
operations, seems on a first view to be a very 
simple affair, in which it would be difficult to go 
wrong, and in which rules would be needless ; and 
yet we find a most ingenious and elaborate system 
of distinctions, maxims, and canons, constructed 
with no other purpose than to ensure its being 
correctly performed. It seems scarcely credible, 
when stated in plain terms, that the scholastic 
logic, with all its formidable apparatus, proposes 
to itself, as its sole ultimate object, to secure the 
correctness and try the validity of the simple 
processes of class-reasoning. Hence this singular 
monument of human ingenuity, dedicated to so 
small an object, would be almost worth a par- 
ticular examination, even if its real character had 
been universally appreciated, and it had been suf- 
fered to take its place amongst the obsolete sys- 
tems of past ages. But since its claims to prac- 
tical importance have been recently revived and 
re-asserted by writers distinguished for their talents 
and learning, an attempt to estimate the value of 
its rules seems an indispensable step in the treat- 
ment of my subject, although it will be giving to 
the question a larger space than in such a treatise 
it ought naturally to occupy. 

I purpose, accordingly, to examine the assistance 
which the scholastic logic affords in the depart- 

K 



130 THE THEORY OF REASONING. 

ment to which its own theory has confined it ; to 
inquire how efficiently it performs its part in the 
limited province which logicians so long mistook 
for the whole domain of reasoning. And when 
(as I further purpose to do) I have followed up 
this examination, and my previous exposition of 
the principles and forms of reasoning, by some 
remarks on the value of the system as externally 
manifested by its effects in action and in science, 
and on its influence as an intellectual discipline, 
I shall have taken a survey of its most important 
features. 

Section III. 

Subject continued: Mode of using the Syllogistic 

Form. 

In order to clear the way for the inquiry proposed 
in the last section, it is necessary to premise that 
there are two different views entertained or enter- 
tainable of the way in which the syllogistic form 
ought to be employed. 

One of these views regards the regular syllogism 
as a method of arguing which is to be commonly 
adopted. 

The other regards it simply as a form into 
which any arguments may be thrown for the pur- 
pose of testing their validity, and disclaims it as the 
ordinary instrument of reasoning or controversy. 

With regard to the first, which was the view 



RULES IN REASONING. 131 

that long prevailed in the schools, it is obvious, to 
modern eyes, that to adopt the syllogism as the 
ordinary method of conducting argumentation, even 
on the supposition of its being the universal type 
of reasoning, would be excessively tedious and em- 
barrassing ; and, indeed, at the present stage of 
intellectual advancement, impracticable. 

This view, accordingly, of the proper method of 
applying the syllogistic art is now not only aban- 
doned, but we are told that "it is a mistake to 
suppose that Aristotle and other logicians meant 
to propose that this prolix form of unfolding ar- 
guments should universally supersede, in argu- 
mentative discourses, the common forms of ex- 
pression." 

Whatever may be the light in which modern 
writers may regard the subject, this prolix form, 
nevertheless, was not only for a long period used 
in the schools, as the most efficient instrument 
of controversy, and the best method of pursuing 
truth, but even so late as the early part of the 
eighteenth century, the utility of carrying on a 
controversy in writing by a mutual exchange of 
syllogisms, and with a strict observance of the 
legitimate forms, was maintained by no less a 
philosopher than Leibnitz. 

Since, however, the common employment of the 
syllogistic form in argumentative discourse or con- 
troversy is no longer advocated, it must be ex- 
amined in the character in which it presents itself 

K 2 



132 THE THEORY OF REASONING. 

to us in the writings of its modern expositors ; 
namely, as a form into which reasoning may be 
reduced in order that the rules of logic may be 
applied as tests for trying the validity of argu- 
ments. Its claims are thus stated by one of the 
most eminent amongst the logical writers 'of the 
day. " Logic," says Dr. Whately, " which is, as 
it were, the grammar of reasoning, does not bring 
forward the regular syllogism as a distinct mode 
of argumentation, designed to be substituted for 
any other mode, but as the form to which all cor- 
rect reasoning may be ultimately reduced ; and 
which, consequently, serves the purpose (when we 
are employing logic as an art) of a test to try the 
validity of any argument ; in the same manner as 
by chemical analysis we develope and submit to a 
distinct examination the elements of which any 
compound body is composed, and are thus enabled 
to detect any latent sophistication and impurity." * 
In this statement, however, of the mode in which 
the form is to be used, the syllogism itself is repre- 
sented as a test, while it manifestly can be con- 
sidered only as the shape into which class-rea- 
soning may be put, in order to apply the several 
tests furnished by the rules of the art. It is not 
the bed on which the logical Procrustes is to lay 
his victims, but only the outstretched posture in 
which he is to place them upon it. 

* Elements of Logic, p. 1 1 



RULES IN REASONING. 133 



Section IV. 



The Subject of Rules continued : Rules of the 
Scholastic Logic. 

Agreeably to what has been stated in the pre- 
ceding section, we are now to consider the scho- 
lastic logic, as a guide to correct conclusions, by 
furnishing tests for the detection of fallacies in that 
variety of reasoning which comes under the desig- 
nation of class-reasoning. 

In this character the system might, perhaps, be 
reasonably expected to do two things ; first, to 
give us directions for reducing, with all prac- 
ticable readiness and precision, the arguments 
which we meet with, or which occur to us, into 
the syllogistic form ; secondly, to furnish us with 
the best rules for testing the validity of the syllo- 
gisms when they are before us. In the first re- 
spect here mentioned, the common treatises on 
logic, as far as I am acquainted with them, afford 
us little help. Logicians may, perhaps, consider 
it as being, like the laying down of premises, out 
of their province ; yet this, after all, is the great 
difficulty which the anxious searcher after right 
conclusions has to cope with. Generally speaking, 
the validity or invalidity of an argument is easy 

to be discerned when it has been stripped of un- 
it 3 



134 THE THEORY OF REASONING. 

necessary incumbrances, and reduced to the form 
of two or three definite propositions.* 

In reference to the second and easier assistance 
which the system ought to furnish, there is no 
similar deficiency. Logical treatises abound with 
rules for insuring the correctness of the syllogistic 
process, and the detection of errors in it. They 
give us copious directions how to deal with any 
syllogisms which may present themselves to our 
notice ; they, in truth, encumber us with help, but 
with help of a peculiarly artificial character. The 
general scope, indeed, of the scholastic system may 
be described to be to enable us, by the adoption of 
technical language and distinctions, to apply me- 
chanical rules to reasoning when it has been 
brought into the syllogistic form. The question 
we have now to try is not between rules and no 
rules, but between natural and artificial rules. 

A recourse to mechanical rules in the way de- 
scribed, which is essentially an artificial method, 
in order to supersede the direct application of the 
mind to the subject in hand, which may be called 
the natural method, is in truth substituting pro- 
cesses requiring little or no thought when once 
learned, for such as demand conscious intelligence 

* Perhaps the student might derive some useful hints 
towards this species of reduction from the Abbe Gaultier's 
ingenious work entitled " A Method of making Abridgments, 
or easy and certain Rules for analysing Authors." London, 
1800, 



RULES IN REASONING. 135 

at every step, and seems eligible only under certain 
conditions. 

If the natural method is sufficiently simple and 
easy, and fully adequate to its purpose, the intro- 
duction of an artificial one is a sheer impertinence, 
entailing waste of time and labour. If, on the 
other hand, such mechanical rules replace a long 
by a compendious process, or a difficult by an easy 
one, or lead us to the desired result with more 
certain accuracy than precepts or principles which 
keep the matter throughout present to our con- 
sciousness, there is a presumptive advantage in 
resorting to their assistance. In these cases, they 
can be wisely rejected only on the ground that 
they are attended with preponderant evils in other 
directions ; and when they enable us to accomplish 
valuable ends, which could not be effected at all 
without them, there can be no question as to the 
wisdom of calling them to our aid. 

Some of the systems of artificial memory, for 
instance, appear to have the merit of enabling 
those persons who use them to remember things 
which they could not otherwise so firmly retain, or 
recollect with equal promptitude and accuracy ; 
but it may be justly objected that this advantage, 
which is at best only one of degree, is dearly pur- 
chased at the expense of connecting our knowledge 
with images and sounds, and other associations, to 
which it has no natural affinity, and thus filling 
the mind with incongruous and fantastic trains of 

K 4 



136 THE THEORY OF REASONING. 

thought. Accordingly, such expedients, except a 
few of the simplest kind, in which the alleged evil 
is not prominent, have fallen into general neglect. 

On the other hand, those technical terms and 
mechanical rules and formulas, which are employed 
in the various departments of calculation, although 
they may not be improving to our principal mental 
faculties, do not, at all events, fill the mind with 
incongruities, while they in some cases substitute 
short and easy processes for longer and more diffi- 
cult ones, and in others enable us to arrive at 
results which we should vainly attempt without 
them. 

That the peculiar assistance which the scholastic 
logic holds out is of this technical and mechanical 
character, no one will probably dispute. Its pro- 
fessed business is to leave out of consideration 
facts and things, and deal with terms and propo- 
sitions ; and these it denudes, as much as possible, 
of meaning, that their most general relations may 
be alone regarded. 

Moreover, after affixing technical acceptations 
to certain words, it constructs rules and symbols, 
by the observance and employment of which we 
may draw our conclusions correctly, without taking 
into view the particular signification of what we 
are reasoning about — without, in truth, any expen- 
diture of thought ; and, of course, by the me- 
chanical application of these rules to the arguments 
of others, we may test their soundness, with a 



RULES IN REASONING. 137 

similar disregard of their special import. The 
questions, then, which we have to consider, are 
whether these mechanical tests are needed, and are 
superior in efficiency to such as we may derive, 
when requisite, from the matter and meaning of 
the reasoning ; and whether they are not attended 
with intellectual disadvantages, which must, in 
any case, render their adoption inexpedient. 

The principal constituent parts of this mechan- 
ical ordeal (and it will not probably be deemed 
requisite to examine any other than these) are the 
rules relating to the distribution of terms, the 
devices and directions for reducing what are called 
imperfect syllogisms to the first figure, and the 
canons or maxims which have been introduced to 
supersede the necessity of such a reduction. 

Our first business, then, will be to examine 
whether the rules relating to the distribution of 
terms furnish any valuable assistance. 

Let us take one of the rules laid down on this 
point, " No term must be distributed in the con- 
clusion, which was not distributed in one of the 
premises ; " and let us apply it to the following 
reasoning : 

All men are mortal ;* 
Angels are not men ; 
Therefore angels are not mortal. 

Now, in order to determine whether this syllo- 
gism is valid by the above rule, you must examine 
the two terms in the conclusion, when you will 



138 THE THEORY OF REASONING. 

find that both of them are there distributed. You 
find, further, that the minor term " angels " is 
distributed in the premises, but that the major 
term " mortal " is not distributed in the premises. 
The rule consequently is violated ; there is what is 
called an illicit process of the major, and the 
syllogism is not valid. 

No doubt that in this way we detect the fallacy ; 
but surely we detect it at once, without passing 
through this examination of the technical con- 
formity of the terms to the logical canon. We see 
from the meaning of the propositions, that the 
argument is unsound, as readily as we discern that 
a term is distributed in the conclusion which is 
not distributed in the premises. A person who 
was unacquainted with the distribution of terms, 
on hearing such an argument, would probably 
exclaim, " Angels are not mortal, because they are 
not men, who are mortal ! Why, the same reason 
would prove that pigs are immortal ! If men were 
the only mortal beings in the universe, the reasoning 
would be good." 

It is obvious that the circumstance of your not 
belonging to a given class is no proof that you do 
not possess any quality in common with the class. 
You are not a cow, but this is no proof that you 
do not breathe. 

The same result will attend an examination of 
the rule which requires the distribution of the 
middle term. I have seen it somewhere argued 



RULES IN EEASONING. 139 

that the very viciousness of Negroes proves them 
to be men. Putting this argument syllogistically, 
and supplying, for the sake of illustration, a major 
premise to suit our purpose, we have, 
All men are vicious ; 
Negroes are vicious ; 
Therefore they are men. 

Here a logician would at once see that the middle 
term " vicious " is not distributed, and would pro- 
nounce the argument unsound. But it is just as 
easy to see that the fact of Negroes being vicious 
would not prove them to be men unless that 
quality were the exclusive attribute of men. 

The logical rule is, that the middle term must 
be distributed, otherwise the syllogism is false. 

The real or material rule is, that the possession 
of one quality, or one set of qualities, in common 
with a given class, does not of itself prove the 
possessors to belong to the class. A cow breathes 
in common with human beings, but this is no proof 
that she belongs to the genus homo. 

The technical rule is not only without any pre- 
tension to be easier of application than the material 
one, but it tends to keep out of sight the substance 
of the fallacy committed. In fact, the system 
puts us in such cases to twofold or threefold 
trouble. We have first to learn the rule and to 
discern its validity, and we have then to apply it 
mechanically to the syllogism before us ; but 
neither of these steps is easier than the immediate 



140 THE THEORY OF REASONING. 

discernment of the substantial error in the rea- 
soning by an equal application of the mind to the 
matter of the argument. 

The rules, nevertheless, regarding the distri- 
bution of terms, and the rules generally regarding 
syllogisms, although such as are merely technical 
might be replaced with advantage by what I have 
called material rules, are, at all events, easy of 
acquisition, as well as capable of being readily 
turned to some account, and hence are by no 
means the most exceptionable features of the scho- 
lastic logic. 

The second class of rules before mentioned, viz., 
those relating to the reduction of syllogisms, and 
to what are denominated the moods and figures, 
which make a great show in logical treatises, con- 
stitute a much more objectionable part of the 
system, demanding wearisome study before any 
one can attain such a familiarity with them as is 
requisite for use, and yielding no fruit but what 
(if I may hazard the metaphor on such a subject) 
is full of the ashes of time thus laboriously con- 
sumed. 

The acknowledged fact to which I have before 
adverted, that every syllogism is not an exemplifi- 
cation of the dictum, or, in the language of lo- 
gicians, that the dictum is not directly applicable 
to every syllogism, led to two different modes of 
proceeding, in order to prove (still to use their 



RULES IN REASONING. 141 

own language) the validity of the reasoning in such 
cases. The first (and this was the method of Ari- 
stotle himself) was to have recourse to the con- 
version of propositions and the transposition of 
premises, for the purpose of bringing every syllo- 
gism that did not exemplify the maxim into a 
shape in which it would, i. e., under what is tech- 
nically called the first figure. 

Thus the scheme of moods and figures, the bar- 
barous phraseology by which the former are desig- 
nated, and the reduction of syllogisms according to 
certain literal indications from one mood and figure 
to another, may be regarded as the progeny of the 
unsound doctrine that all reasoning proceeds on 
one principle, and of the supposed necessity of 
bringing all arguments under it. 

In the chapter on the general principles of 
reasoning, I have shown that each figure or variety 
of syllogism proceeds on, or exemplifies, its own 
principle ; and such being the case, if it is neces- 
sary, on any occasion, to appeal, after the manner 
of mathematicians, to any axiom, the particular 
maxims belonging to the figure may be cited, 
without resorting to the intricate machinery for 
transmuting one form of argument into another. 

Let us examine, nevertheless, what this process 
of reduction effects. Take an example from Dr. 
Whately. He gives us the following syllogism in 
the mood Camestres, as one to be reduced : 



142 THE THEORY OF REASONING. 

All true philosophers account virtue a good in 

itself ; 
The advocates of pleasure do not account 

virtue a good in itself; 
Therefore they are not true philosophers. 
One would think this sufficiently plain ; but it 
does not come within the first figure. It must, 
therefore, be brought into a mood which does. 
Keduced to the mood Celarent by conversion and 
transposition, the syllogism assumes the following 
appearance : 

Those who account virtue a good in itself are 

not advocates of pleasure ; 
All true philosophers account virtue a good in 

itself ; 
Therefore no true philosophers are advocates 
of pleasure. 
But still the conclusion we have got is not the 
original conclusion ; and, in order to show that we 
have obtained an equivalent one, we must force it 
to undergo illative conversion, when it will emerge 
in the form of, No advocates of pleasure are true phi- 
losophers ; which must, in its turn, be transmuted 
by a slight alteration into the equipollent and pris- 
tine proposition, The advocates of pleasure are not 
true philosophers; and, at length, our work is done. 
It is manifest that here, after all this logical 
labour and circuitous ingenuity, we gain nothing. 
The syllogism, which issues out of the operation, 
is not in the slightest degree clearer than the ori- 
ginal one. 



RULES IN REASONING. 143 

So much for the first method of getting over the 
inapplicability of the dictum to the second, third, 
and fourth figures. The second method was to 
allow the refractory syllogisms in these figures to 
retain their forms, and to call in the aid of other 
principles or maxims which might be directly 
applied to them. Discarding altogether the process 
of reduction, it borrowed two mathematical axioms, 
changing the term equality to that of agreement. 
They are, "if two things [or terms] agree with 
one and the same third, they agree with each 
other ; " and " if one thing [or term] agrees, and 
another disagrees, with one and the same third, 
they disagree with each other." 

If these maxims are taken in their obvious ac- 
ceptation, they are such as many of our common 
reasonings exemplify. Thus we sometimes argue 
that two objects agree in form, colour, smoothness, 
temperature, resplendence, and other qualities, be- 
cause they have been severally compared with a 
third object, and found to resemble it in these 
respects. In this acceptation they further elu- 
cidate the truth, that demonstration proceeds on a 
variety of principles besides the dictum. 

But this is not the sense in which the logical 
canons are to be understood. The phrase, " Agree- 
ing with a term" is to be taken in a peculiar tech- 
nical acceptation; and unless certain rules re- 
specting the comparison and agreement of wholes 
and parts of terms are understood and observed, the 



144 THE THEORY OF REASONING. 

maxims, as they are called, are neither evident 
nor applicable. 

It is obvious that these maxims, so interpreted, 
are not analogous to such as were considered in the 
chapter on that subject. They are not educible 
from the syllogisms' in any of the figures; nor are 
they to be classed with the mathematical axioms 
from which they have been transformed. Bearing 
the semblance of self-evident maxims, they are, in 
truth, very artificial rules by which, with the help 
of other rules, and technical distinctions, the va- 
lidity of syllogisms may be tested.* 

* Logicians are far from being agreed as to the merits of 
the method here described. "Wallis speaks of it in the following 
terms : " Nonnulli autem Logici (nostri seculi aut superioris) 
posthabita veterum probatione per Dictum de Omni et de JNullo ; 
aliud substituunt illius loco postulatum ; nimirum, Quce con- 
veniunt in eodem tertio conveniunt inter se. Atque ad hanc 
regulam exigentes singulos syllogismorum modos, inde con- 
clusion eunt justam eorum consecutionem. Quique sic proce- 
dunt, negligere possunt earn distinctionem modorum perfectorum 
et imperfectorum ; ut quae ortum ducit ab ea methodo qua usi 
sunt veteres, in probatione sua ab illo Dicto. Ego veterum 
probationem ut potiorem amplector, Aristotelis methodo con- 
formem." — Institutio Logicce, lib. iii. cap. 5. 

It may be well to subjoin Mr. "Walker's commentary on this 
method. " But clear as these principles are in mathematics, 
when transferred by analogy to the agreement or disagreement 
of terms or ideas, in affirmative or negative propositions, they 
by no means have that definite and certain meaning which is 
necessary in principles that are taken for the basis of such a 
superstructure as. the doctrine of syllogisms. Aristotle had too 
much penetration to rest the doctrine on this foundation." — 
Commentary on the Dublin Compendium of Logic, by John 
Walker, 4th ed., p. 93. 



RULES IN REASONING. 145 

It is needless, perhaps, to task the reader's 
patience by any detail in reference to this second 
method. In order, however, to complete the sur- 
vey of these mechanical aids, I will adduce a single 
example of the way in which it is carried into 
effect. 

Let the syllogism to be put on its trial be the 
following : 

Some logical writers are tedious ; 
Wallis is a logical writer ; 
Therefore Wallis is tedious. 

Here the major term, tedious, has been com- 
pared to only a part of the middle term, logical 
writers ; and the minor term, Wallis, also to only a 
part of it. And since these two parts, for aught 
that appears, may be different portions of the same 
whole, it cannot be affirmed that the major and 
minor terms have been compared with one and the 
same third, nor, consequently, that they agree with 
each other. The canon has not been complied with, 
and the conclusion does not follow from the pre- 
mises. Wallis is not proved to be a tedious writer. 

This is all very true ; but it is a very round- 
about method of detecting a fallacy which is ob- 
vious on a bare inspection, or which may be made 
apparent, if any aid be wanted in so plain a case, 
by a simple material rule ; or which may be made 
readily proved even by resorting to the rule which 
requires the distribution of the middle term. 

As a method of testing syllogisms, it is scarcely 

L 



146 THE THEORY OF REASONING. 

less intricate, and not more satisfactory, than the 
other methods already examined. 

From the whole of this, I fear, wearisome inves- 
tigation, it results that the logical system will not 
bear the criteria applied to it. 

Such an artificial system is needless, because 
the natural method is ready of application, and 
sufficient of itself. It does not substitute com- 
pendious processes for long ones, nor such as are 
easy for such as are difficult, nor those which are 
more certain for those which are less to be relied 
upon; and it has not the slightest pretensions to 
the power of conducting us to results which we 
could not reach without its assistance; while, on 
the other hand, the study of it requires a great 
expenditure of time and labour, and, as I shall en- 
deavour to show hereafter, is attended, from its very 
nature, with intellectual evils of no inconsiderable 
moment. 

Section Y. 

The Subject of Rules continued : Rules of the 
Scholastic Logic, 

From the preceding examination it appears that 
there are only two or three errors worth notice 
which all these distinctions and canons have been 
devised to guard us against*; and, in the course 

* I have not taken cognizance of the rules about negative 
premises and the infraction of them, because they seem to be 



RULES IN REASONING. 147 

of it, the obvious truth has been pointed out, that, 
if rules are at all necessary or useful, a few easy 
material rules would serve the purpose. 

But I have very strong doubts whether the 
errors in question are ever committed except from 
confusion or ambiguity of language, or possibly 
from such a separation of the premises from the 
conclusion as may occasion a misrecollection of 
what they are ; in each of which cases no assist- 
ance could be derived from logical rules. 

A valid syllogism, when clearly expressed, is 
discerned at once to be valid. The conclusion is 
seen to be demonstrated by the premises, and a 
denial of it to involve a contradiction. The 
validity of the syllogism itself is a thing beyond 
proof. 

But if a valid syllogism is, in this way, discerned 
to be conclusive, a fallacious syllogism w T ould, in 
the same way, be at once discerned to be fallacious 
or inconclusive, under the same condition, viz. 
when clearly expressed. 

It follows that, when faults are committed in 
syllogistic reasoning, they must be owing to want 
of clearness and preciseness of expression ; and the 

passed over by logical writers with the barest mention. Indeed, 
the purely logical fallacies, to guard against which the artificial 
system just examined is solely applicable, are allowed to 
occupy very little space in most treatises on the subject — and 
deservedly: but the reader is constantly wondering why so 
complicated an apparatus is introduced for an end apparently 
so small in itself and so little thought of by its expositors. 

L 2 



148 THE THEORY OF REASONING. 

infallible way to test the soundness and unsound- 
ness of such reasoning is to supply what it wants — 
to throw it into precise and perspicuous language. 
This must be sufficient, in the nature of the case, 
to bring all errors to light. 

It may be presumed, therefore, that the fallacies 
which we have already passed in review under the 
names of non-distribution of the middle term and 
illicit processes, when they do occur in regular 
syllogisms, are owing to ambiguity or confusion of 
language: in other words, they are never com- 
mitted when the premises are fully and clearly 
stated in proper juxtaposition with the conclusion. 
Let us take an example of the non-distribution of 
the middle term. 

Some animals are cold-blooded ; 
The sheep is an animal ; 
Therefore the sheep is cold-blooded. 

In a syllogism expressed in this clear unam- 
biguous manner, such a conclusion may be safely 
pronounced to be impossible. 

It may be instructive to remark, that the only 
discernible or assignable difference between such a 
logical fallacy, and drawing an unwarranted infer- 
ence from an insufficient induction of facts, is, that 
in the latter case, the " some animals " adduced 
are avowedly, although erroneously, taken as suffi- 
cient specimens of the rest, and contradictory in- 
stances are assumed not to exist ; whereas, in the 
logical error, this is not professedly assumed : the 
fact of some animals being cold-blooded is alleged 



KULES IN REASONING. 149 

as a sufficient reason (although it is not pretended 
that there are not also some animals which are 
warm-blooded) for concluding any other animal to 
be so. But a logical error of this kind is so very 
absurd, that it is doubtful whether any human 
mind ever really committed it, the actual mistake 
being either an insufficient induction, or a fault in 
expression.* 

There is the case, indeed, of disparted premises 
and conclusion already named, in which we may 
conceive that the logical error might possibly 
occur, or seem to occur. It sometimes happens 
that the premises and the conclusion of an argu- 
ment are widely separated from each other by 
irrelevant matter, superfluous- verbiage, or prolix 
dissertation, so that, when the conclusion is ar- 
rived at, the premises are but indistinctly recalled : 
and thus the reasoner himself may be betrayed 
into an inference which they will not support, and 
into which the reader will in all likelihood supinely 
follow him. This, however, is misrecollection or 
misconception of what the premises really are, and 

* Mr. Hallam is the only logician, as far as I know, who has 
remarked in such instances the close similarity of the inductive 
to the logical error, and the circumstance of one being some- 
times confounded with the other. He observes that " the as- 
sertion of a general premise upon an insufficient examination 
of particulars " " is the error into which men really fall, not that 
of omitting to distribute the middle term, though it comes in 
effect, and often in appearance, to the same thing" — Intro- 
duction to the Literature of Europe, vol. iii. p. 220. 

l 3 



150 THE THEORY OF REASONING. 

not a wrong inference from them; nor could the 
error be prevented or detected by any logical rule ; 
but if the argument were freed from its encum- 
brances, and premises and conclusion, clearly ex- 
pressed, were brought into juxtaposition, the bad 
reasoning would be too manifest to impose upon a 
child. 

Let us next take an example of the illicit pro- 
cess of the major term. 
All vegetables grow ; 
Animals are not vegetables ; 
Therefore animals do not grow. 

Is it conceivable that any one could commit a 
fallacy of this nature ? — that a naturalist, for 
example, after collecting instances to show that a 
class possess a certain quality, should adduce this 
collective fact in proof that a totally different class 
do not possess it ? Surely, absurdities of this 
kind, of which no one is likely even to approach 
the brink, are beneath the attention of the logical 
legislator. Eules devised as a safeguard against 
mistakes which there is no danger of a sane mind 
falling into may be multiplied without end, but 
they can form only a dead weight on the system 
into which they are introduced. 

If logical errors are thus owing, in all cases 
(except in the peculiar case of separated premises 
and conclusion), to faults of expression, what as- 
sistance does the scholastic system afford for guard- 
ing against this source of fallacy? None, I am 



RULES IN REASONING. 151 

persuaded, worth regarding. It is not even pre- 
tended that it affords much. 

It has, indeed, been urged by some writers that 
the canons of the scholastic logic assist us to dis- 
cover them by directing our attention to the 
middle term, in which any ambiguity is most 
likely to lurk, as may be seen, they say, in such 
syllogisms as the following : — 

Light is contrary to darkness ; 

Feathers are light ; 

Therefore feathers are contrary to darkness. 
Here, doubtless, the ambiguity is in the middle 
term ; but the middle term has not, unfortunately, 
a monopoly of equivocation. It is just as easy, by 
an ambiguous major term, to prove another extra- 
ordinary quality in feathers : — 

All bodies are heavy ; 

A feather is a body ; 

Therefore a feather is heavy. 
The truth is, that in reasoning we are never safe 
without a constant scrutiny of all the words we 
employ, i, e. without a perpetual recurrence to the 
things signified ; and if our attention is directed 
to the middle term more especially than to the 
other terms, we may be led to overlook ambiguities 
in the latter which might not otherwise escape us. 
All this once more forces upon our minds the 
immense contrast between the elaborate apparatus 
of the scholastic logic and the inconsiderable end 
achieved by it ; guarding us, at the utmost, from a 

L 4 



152 THE THEORY OF REASONING. 

few mistakes in which there is scarcely the slightest 
risk of our being involved except from causes of 
error which it is powerless to obviate or to remedy. 

These views coincide with those which appear 
to have been entertained by the authors of the 
" Port Eoyal Logic," though not perhaps with 
uniform consistency. 

"If we ever sin," they remark, " against the 
rules of syllogism, it is by deceiving ourselves 

with the equivocation of some term 

Not but that there are still other vices of reasoning 
besides that which springs from the equivocal 
meaning of terms, but these it is almost impossible 
for a man of average mind, and possessed of some 
knowledge, ever to fall into, especially in speculative 
matters, and thus it would be useless to give rules 
against these vices and urge their observance ; and 
it would, indeed, be frivolous, since the application 
which would be given to these superfluous rules 
might divert the attention which we ought to pay 
to things more necessary."* 

Although I have thus been led to an unfavour- 
able appreciation of the system, particularly of the 
technical and mechanical apparatus peculiar to it, 
I will readily admit that there are some points 
about it which deserve preservation. 

Few will question that the logic of Aristotle and 
his followers furnishes a number of useful as well 

* Port Royal Art of Thinking, part iv. chap. 8. In this 
extract I have availed myself of Mr. Baynes's translation. 



RULES IN REASONING. 153 

as useless distinctions relative to words and pro- 
positions ; and many convenient terms for desig- 
nating the parts and incidents of argumentation, 
including the different kinds of fallacies into which 
a reasoner is apt to fall. Many, however, of these, 
indeed most of them that can be considered of 
importance, are independent of any peculiar theory 
of reasoning, and may be regarded as of common 
use. 

It must be also admitted, that the syllogistic 
form may be usefully employed on some occasions, 
without the reasoner troubling himself with any of 
the technicalities of the system. We have already 
seen that much reasoning does exemplify or proceed 
upon the dictum de omni et nullo or other allied 
dicta, and that many arguments which are usually 
expressed in the form of enthymemes may be 
rightly expanded into syllogisms. To draw out 
such arguments, when it is needful to examine 
their accuracy, into three separate propositions 
enables us to see distinctly, and to point out to 
others, the facts which must be true, or proved, or 
admitted, in order to render the conclusion valid. 
It is a method of spreading out the premises before 
us, which may be occasionally resorted to with 
advantage, even by those who would discard the 
syllogism as the shape into which every argument 
might be legitimately thrown, and who would 
reject all mechanical contrivances for securing a 
correct conclusion. 



154 THE THEORY OF REASONING. 

Here, however, we are supposing an enthymeme 
ready to our hands, while in ordinary cases the 
chief difficulty, as I have before remarked, would 
lie in reducing the argument into two or three 
distinct propositions, not in perceiving the force or 
the fallacy of the reasoning, when brought into 
such a regular and definite shape. 

We have been hitherto engaged with what may 
be termed the internal merits and demerits of the 
system ; but it may be instructive to cast a glance 
on its external effects, or, in other words, its prac- 
tical value in action and science. 

Amongst the most plausible attempts to vindi- 
cate the practical value of the syllogistic art, is 
one to be found in the commentary of Mr. Walker 
on the " Dublin Compendium of Logic," in which 
he has contrasted the position of an adept in the 
art when engaged in controversy, and that of an 
antagonist wholly ignorant of it. 

" A real acquaintance," he says, " with the art 
of logic will abundantly compensate the labour of 
acquiring it. Nor have I ever met a person un- 
acquainted with it, who could state and maintain 
his arguments with facility, clearness, and pre- 
cision. To instance only in one of the occasions 
to which it may be applied: — I have commonly 
seen a man of the acutest mind puzzled by the 
argument of his antagonist ; sensible, perhaps, 
that it was inconclusive, but wholly unable to 
expose the fallacy which rendered it so ; while a 



RULES IN REASONING. 155 

logician, of perhaps very inferior talents, would be 
able at once to discern and to mark it. It was 
happily remarked by a late lawyer of eminence, 
in a letter to his son, that nothing is superior to 
logic for setting a fine edge on the understanding."* 

Although the correctness of this contrast were 
to be admitted, the most important point would 
still be left untouched. 

The logician described might, doubtless, possess 
a superiority over an antagonist who had never 
attended to the nature of reasoning at all, or who 
was not familiar with its different phases ; but, 
let us ask, how would he compare with one who 
had studied the subject in the pages of Locke and 
Stewart, or in the light in which it has been the 
aim of this treatise to place it ; whose mind had 
been familiarised with what we are told the scho- 
lastic logic disowns — the scrutiny of premises, and 
with the processes of direct contingent reasoning, 
and especially the formation of general laws from 
collected facts ; who was capable of discerning 
the exact range of the scholastic system; who 
could discriminate a major premise arrived at by 

* Familiar Commentary, p. 4. It may amuse the reader to 
compare Mr. Walker's testimony with that of Locke. " I have 
known," the latter says, " a man unskilful in syllogism, who at 
first hearing could perceive the weakness and inconclusiveness 
of a long, artificial, and plausible discourse, wherewith others 
better skilled in syllogism have been misled. And I believe 
there are few of my readers who do not know such." — Essay on 
Human Under standing, book iv. chap. xvii. 



156 THE THEORY OF REASONING. 

a process of induction, from a useless maxim 
forced into the same position upon an already 
effective enthymeme, like a crutch thrust into 
the hands of a perfectly sound man; and who, 
through the mere forms of reasoning, could see 
whether an inference was to be regarded as con- 
tingently or conclusively demonstrated ; who, in a 
word, had within him a distinct consciousness of 
what he was about, of the nature of the processes 
in his own mind, and a clear view of the bearing 
of the implicated facts, independently of the forms 
and phraseology in which they might be expressed ? 

Although one who had studied an erroneous 
theory, and an art founded upon it, in which 
there would probably be a mixture of truth and 
error, might carry off the palm in a contest with 
an adversary who had paid no attention to the 
nature of reasoning at all, it is allowable to sup- 
pose that he would, in his turn, find himself 
inferior to another antagonist who was master 
of a more correct theory than his own. 

But a still more important question remains : 
which of the two would be likely to have greater 
success, not in mere personal controversy, but in 
the pursuit of truth, in the prosecution of science, 
in the estimation of evidence, and in drawing with 
accuracy those numberless conclusions which are 
required from every one by the daily exigencies of 
life? 

It may be considered as a remarkable circum- 



KULES IN REASONING. 157 

stance, in confirmation of these views of the small 
practical value of the scholastic logic, that in the 
rapid progress of science which has marked the last 
two hundred years, it appears to have had no share 
and to have yielded no assistance; nor have we 
any evidence that the greatest philosophers and the 
most effective reasoners either in practical or specu- 
lative matters (Leibnitz perhaps excepted) had so 
much as a tolerable acquaintance with it. Some of 
them have even been accused of evincing by oc- 
casional errors in their casual references, or their 
depreciating comments, how little they understood 
what they referred to or assailed. 

Even those writers who have recently attempted 
to revive the attention of the world to its merits 
seem to have contented themselves with a theo- 
retical advocacy of its claims ; for their writings 
furnish few proofs that its technical distinctions and 
mechanical rules have been pressed into actual 
service. A casual notice here and there that some 
syllogism which they are employing or commenting 
upon, ranks under Barbara or Baroko, is all that 
we meet with. 

Should it be replied to this allegation, that these 
logicians may nevertheless have been tacitly guided 
by its rules, although they have not allowed the 
fact to appear ; the reply may be admitted as pos- 
sibly true, although not very probably so, while we 
have the opposing testimony of no less an authority 
than Dr. Whately, who, in a remarkable passage, 



158 TEIE THEORY OF REASONING. 

has told us that " the generality of logical writers, 
whenever they have to treat of any thing that is 
beyond the mere elements of Logic, totally lay aside 
all reference to the principles they have been oc- 
cupied in establishing and explaining, and have 
recourse to a loose, vague, and popular kind of 
language." * Can there be a more complete sur- 
render of the practical value of all that is peculiar 
in the art ? f 

The case of the mathematicians, however, is on 
the whole, perhaps, the most striking. 

Although many of the steps in geometrical 
reasoning (all of them according to the logicians 
themselves) may be brought under the dictum de 
omni et nullo, and thus fall within the domain of 
formal logic, it is notorious that no use of the scho- 
lastic rules and distinctions is ever made in this 
great department of demonstrative science, in which 
we never hear of undistributed middles, illicit pro- 
cesses, moods and figures, and reduction of syllo- 
gisms. J Nothing surely can be a stronger external 
proof of the limited utility, not to say the utter 

* Elements of Logic, p. 133., 1st ed. 8vo. 

f The following testimony to the want of adaptation in the 
art to the requirements of intellectual beings is curious. 
" Experience shows," say the authors of the Port Eoyal Art of 
Thinking, " that of a thousand young men who learn logic, 
there are not ten who remember anything of it six months 
after having finished their course." — Discourse ii. 

J It is a remark of D'Alembert's, " que les geometres, ceux 
de tous les philosophes qui se sont toujours le moins trompes, 



RULES IN REASONING. 159 

inefficiency, of the technicalities and mechanism of 
the logical system. It is plain that the highest, 
the most accurate, the most recondite, as well as 
the most popular reasoning in the world goes on 
without their assistance. 

Section VI. 

Subject of Rules continued : Effects of the Scholastic 
System as a Discipline of the Mind. 

From the preceding survey of the subject, it is 
apparent not only that technical rules, by which 
operations of a mechanical character may be em- 
ployed to test the validity of arguments, are ex- 
ceedingly limited in their application, and, when 
they can be applied, are useless or less useful than 
rules founded on the matter or signification of the 
reasoning ; but that in argumentative discourse 
and the prosecution of science they are found to be 
practically of little or no value. 

But this negative condemnation is not all. They 
are positively evil, not only by all the trouble and 
perplexity which they needlessly occasion, but in 
a still higher degree by withdrawing attention from 

ont toujours ete ceux qui ont fait le moins de syllogismes." — 
Elemens de Philosophie, v. Logique. 

" It does not appear," says Dr. Reid, " that Euclid, or 
Apollonius, or Archimedes, or Huygens, or Newton, ever made 
the least use of this art ; and I am even of opinion that no use 
can be made of it in mathematics." — Analysis of Aristotle's 
Logic, chap. iv. section 5. 



160 THE THEORY OF REASONING. 

the substantial nature of all ratiocination, and 
fixing it exclusively or mainly on the adjustment 
of terms and propositions. This may, perhaps, be 
characterised as the grand evil of the Aristotelian 
Logic, by which it has stunted the minds and 
fettered the progress of the most intelligent nations. 

It is an important truth too generally overlooked, 
that the habitual application of such mechanical 
rules as those we have examined leads the mind 
away from the due appreciation of the realities 
with which reasoning has to do ; from the ex- 
amination of objects, and the investigation of 
events. It has somewhat of the same effect in 
diverting the mind from the consideration of facts, 
that the study of the rules of Latin prosody with 
the exercise of making verses according to those 
rules, has in turning it aside from attention to the 
rhythm and euphony of the lines. The student 
may become exceedingly familiar with the rules 
for long and short syllables, and expert in con- 
structing verses with the legitimate feet, while his 
taste and skill in metrical melody remain unculti- 
vated ; for instead of being guided by the quality 
of the sounds, he directs his course, in a great 
measure, by distinctions founded on the termination 
of syllables and the juxtaposition of letters; dis- 
tinctions which have, to modern ears, no direct 
effect on the music of the verse, or, at all events, 
may be observed without any reference to it. 

How different is the composition of verse by a 



RULES IN REASONING. 161 

poet in his native tongue ! He is not under the 
influence of mechanical rules, but follows the im- 
pulse of his rhythmical taste and feelings, or con- 
forms to principles founded on the observed effects 
of articulate sounds, or of emotions in modulating 
their cadence ; and hence there is naturally a pro- 
gressive improvement in the delicacy of his dis- 
crimination, and in his power of skilfully arranging 
the march of his verse. 

And so in reasoning. Trained in the distinctions 
of technical logic, a man may become dexterous 
in the conversion of propositions, and at home in 
moods and figures ; he may show himself ready in 
the detection of fallacies in form, in finding out 
the non-distribution of middle terms, and tracing 
illicit processes of the minor and the major, at 
least in syllogisms which are prepared to his hands 
in books or invented for the sake of illustration; 
while, in all this, the faculty of looking at facts, 
estimating their value, discovering what they prove, 
and extricating them from any verbiage in which 
they may be involved, which would have been 
exercised and invigorated by an attention to the 
material principles of reasoning, remains compara- 
tively unexercised. 

No one, I think, can look into the writings of 
the scholastic logicians without being struck with 
this tendency of the system to withdraw the at- 
tention from things and fix it upon words. When 
they describe the syllogism, for example, as con- 

M 



162 THE THEOEY OF REASONING. 

taining three terms, the extremes and the middle ; 
when they tell us that each of the extremes is to 
be compared with the middle term in order to 
judge of their mutual agreement or disagreement ; 
that the middle term must be distributed once at 
least ; that no term must be distributed in the 
conclusion which has not been distributed in the 
premises ; that there must not be four terms ; that 
the validity of the argument must be manifest from 
the mere force of the expression, without consi- 
dering the meaning of the three terms; — in such 
descriptions and rules, they do all that is possible 
to engross the mind with words and nothing else. 

Not a whisper in all this of facts, objects, events ; 
the whole proceeding, according to their own re- 
presentation, is an arrangement and comparison 
of signs without attending to their signification. 
What can put realities more completely out of 
sight ? Instead of being taught to look at the 
character and relations of the facts about which 
the reasoning is employed, the young logician is 
instructed to attend to the most general relations 
of the words, and he naturally falls into the habit 
of resting, as far as possible, upon mere forms of 
expression. 

The rules of Latin Prosody, the canons " r Jinita 
corripiuntur" u in b, d, t, desinentia hrevia sunt" 
" producuntur monosyllaba in e," and the rest, are 
assuredly as much adapted to train the ear to a 
nice perception of metrical melody, as this logical 



RULES IN REASONING. 163 

system to strengthen the masculine efficiency of 
our reasoning powers in dealing with the important 
questions of moral, political, and philosophical 
science, or the multifarious business of actual life. 

Kegarded as a discipline of the mind, indeed, 
I cannot see why the arguments brought against 
the study of some departments of mathematics 
should not be brought against the study of techni- 
cal logic. The latter appears to me to be nearly, 
in this respect, in the position of the modern cal- 
culus, the formulae of which have been said to 
transport the mathematician from the data to the 
conclusion in a carriage with the blinds clown ; 
unlike geometrical demonstration, which compels 
him to walk over every inch of the road, and be 
cognizant of every step in his journey. 

But the modern calculus, although it may be of 
questionable value as a discipline of the mind, is 
unquestionably a most powerful and an indis- 
pensable instrument for attaining results which 
pure geometrical operations could never reach; 
while technical logic is not only equally low in 
value as an intellectual exercise, but is besides a 
clumsy and circuitous method of arriving at its 
proposed ends. 

Placed in a scene where we are surrounded by 
objects and immersed in events, we are perpetually 
obliged to reason about them. 

To train the mind to do this by directing its 
attention upon words, to the completest practicable 



164 THE THEORY OE REASONING. 

exclusion of things, through the medium of a 
verbal and literal mechanism, however ingenious, 
instead of habituating it to face realities and 
question their significance, seems to me to unfit 
it for the business in which it is destined to be 
engaged. 

In former times, when the Aristotelian system 
had no rival in physical investigation, the bad 
effects here traced were seen in all their extent; 
but fortunately in our own day the mischievous 
influence of such a discipline is greatly counter- 
acted by the far different discipline of sciences, in 
which no step of reasoning can be taken without 
bringing into view the actual phenomena of life 
and nature. 



ERRONEOUS CONCLUSIONS. 165 



CHAP. XII. 

THE SOURCES OF ERRONEOUS CONCLUSIONS. 

From the survey which we have now taken of the 
field of reasoning, we shall be prepared to enter 
upon that most important question to which any 
theory on the subject of this treatise necessarily 
leads, viz. " what are the sources of erroneous 
conclusions ? " * 

.Reasoning consists in coming to conclusions, and 
the sole legitimate object of the process is to come 
to such as are correct. Why we do not always 
succeed in attaining this end it must be instructive 
to inquire. By erroneous conclusions I here mean 
false propositions at which we have arrived by in- 
ference, whatever may have been the sources of the 
error, whether false facts in the premises, or some 
false step in the reasoning process itself. This 

* I have not entered into the consideration of fallacies 
except in so far as the subject of this chapter required it, 
partly because a minute exposition of them belongs rather to 
the art than to the theory of reasoning, and partly because 
they have been very excellently and fully explained by several 
modern writers, particularly by Dr. Whately and Mr. John 
Mill in their works already referred to, and by Mr. De Morgan 
in his " Formal Logic." 

m 3 



166 THE THEORY OF REASONING. 

remark indicates two of the great sources of erro- 
neous conclusions, viz., wrong facts or premises, 
and wrong processes of inference. 

When we undertake a journey, we may fail to 
reach the proposed end, either by setting out in a 
wrong direction, or, if we set out right, by de- 
viating from the true path in the course of our 
progress. 

In contingent, as indeed in all other reasoning, 
the premises are of course wrong when the facts 
asserted in them are either wholly or partially 
incorrect. We may, from inaccurate observation, 
or misconception, or misrecollection, or other causes, 
be led to propound that all A's, as far as our know- 
ledge has extended, have been found possessed of 
the attribute B, when, in truth (to take an extreme 
case), no A's have been found to possess that at- 
tribute. 

If from such false observation, or undue assump- 
tion, we proceed to infer that all A's possess B, or 
that any unobserved A possesses B, it is an in- 
stance of an erroneous conclusion, of which the 
source is an erroneous premise. 

On the other hand, the process of inferring a 
conclusion in contingent reasoning is wrong when 
the facts contained in the premises, although they 
are correct, are not sufficient to warrant the in- 
ference we draw from them. 

Thus we may lay clown a universal law in the 
form of, all A's possess the attribute B, when the 



ERRONEOUS CONCLUSIONS. 167 

facts warrant us only in the inference that all A's 
probably possess the attribute B. 

The universal law in this case would not be a 
false conclusion from false facts, but would proceed 
from an erroneous estimate of what the correct 
facts of the case enable us legitimately to infer. 
It would be an instance of undue or unwarranted 
generalisation. 

In demonstrative reasoning there are two cases 
to be noted. 

In such as consist of one premise, of the nature 
of a minor, and an inference, erroneous conclusions 
are scarcely possible, except from false facts ; and 
these latter are almost excluded from the principal 
species of such reasoning, viz. mathematical, by 
the circumstance that the facts about which it is 
conversant are few and simple. 

With the greater part of syllogistic reasoning 
the case is otherwise. Here erroneous conclusions 
may proceed both from wrong premises and from 
wrong processes of inference. The wrong pre- 
mises, as in the case of contingent reasoning, 
assert false facts, and frequently owe their origin 
to false general laws obtained by such reasoning ; 
but in a far greater proportion they may be traced 
to pure gratuitous assumption of general propo- 
sitions which are not true. 

The wrong processes of inference, or at least the 
only ones claiming attention, are of two kinds, 
technically called non-distribution of the middle 

M 4 



168 THE THEORY OF REASONING. 

term, and illicit processes of the major and minor 
terms, which I have endeavoured to show are never 
committed when the propositions of a syllogism are 
clearly before the mind, and which may therefore 
be referred to the head of errors attributable to 
the ambiguity or confusion of terms* 

This brings before us the third great source of 
erroneous conclusions. Every species and variety 
of reasoning are liable to be vitiated, and their 
conclusions rendered erroneous, by the imperfec- 
tion of language as an instrument of thought and 
communication ; but less so in proportion as the 
subjects of the reasoning are simple. In mathe- 
matical demonstration, indeed, this disturbance 
may be said to be nought ; while in contingent and 
class-reasoning generally it extensively prevails. 

This imperfection of language produces its fal- 
lacious results chiefly when the terms employed 
are complex, general, or abstract ; and when the 
reasoning is complicated, immethodical, disjointed, 
and verbose. When, on the contrary, the words 
are simple and concrete, and the reasoning is 
well arranged and condensed, it has little room to 
operate. 

From this brief glance at the subject, we may 
gather that the three great sources of false con- 
clusions are imperfections in language, insufficient 
induction of facts, and the assumption of false 
facts, or, to vary the expression, of fictitious pre- 
mises. 



EEEONEOUS CONCLUSIONS. 169 

Their comparative importance appears to me to 
be in the inverse order in which they are here 
mentioned, and that of the last to be by far the 
greatest of all. The few remarks upon them which 
follow will, however, serve to illustrate their abso- 
lute rather than their comparative influence. 

The imperfections of language are universally 
allowed to have great effect in perverting our con- 
clusions ; and it is acknowledged and regretted that 
rules and formulas can do little in guarding against 
them. Habits of mind, nevertheless, can do a great 
deal. 

But by the term imperfections must be under- 
stood not mere equivocation of words, but the 
vagueness, and obscurity, and unmeaningness of 
language, all of which are to be sedulously guarded 
against; and the best preservative against these 
evils is an intellectual habit, quite opposed to that 
which it is the tendency of the scholastic logic to 
engender, — the habit of calling vividly to mind the 
objects, and qualities, and events designated by the 
phrases employed ; of dwelling upon the full and 
precise meaning of all the words on which our 
reasoning turns ; of picturing to ourselves what- 
ever is described or narrated ; of turning the ab- 
stract into the concrete, and reducing the general 
to the particular. This practice, on all important 
occasions, would save us from a thousand illusions 
which the custom of being satisfied with vague and 



170 THE THEOEY OF SEASONING. 

indistinct conceptions, or even with such abstract 
generalities as may be all that, in the eye of logic, 
the reasoning we are engaged with can require, 
creates and perpetuates. 

" Unless," says Berkeley, " we take care to clear 
the first principles of knowledge from the embarrass 
and delusion of words, we may make infinite rea- 
sonings upon them to no purpose ; we may draw 
consequences from consequences, and be never the 
wiser. The further we go, we shall only lose our- 
selves the more irrecoverably, and be the deeper 
entangled in difficulties and mistakes."* 

The second source of erroneous conclusions before 
specified may be justly considered as equal, if not 
superior, in importance to the first, and extensively 
pervades the thoughts and language of mankind. 
Men are constantly in the habit of drawing general 
conclusions from instances too few in number, or 
too incompletely sifted, to warrant them ; in other 
words, from an insufficient induction of facts.f 

A traveller visiting an unknown country re- 
marks, in the first few persons he encounters, some 
peculiar quality or habit, and immediately sets it 
down as a national characteristic. An historian 



* Of the Principles of Human Knowledge. Introduction. 

f " The false inductions by which general propositions are 
derived from some particular experiences, constitute one of 
the most common sources of fallacious reasonings." — Port 
Royal Art of Thinking y part iii. chap. xx. 



ERRONEOUS CONCLUSIONS. 171 

comes upon an event which happens to have been 
ushered in by certain preliminary circumstances; 
and he forthwith assumes it as a general law, that 
such circumstances are the invariable precursors of 
such events. Medical practitioners, and especially 
such as are proverbially said to have fools for their 
patients, will frequently consider a single instance 
of recovery from disease after the administration 
of a particular drug, as sufficient to establish the 
universal efficacy of the medicine in similar cases. 

I have cited illustrations of this familiar character, 
because the great field now for errors of this de- 
scription is not to be found in physical science, but 
in common life. Such fallacies form one of the 
main characteristics of loose thinking in the bulk of 
mankind. But these undue generalisations are not 
seldom found in systematic writers on moral and po- 
litical philosophy ; and it is sometimes amusing to 
notice the subsequent fallacies which flow from them. 
The law enunciated ought, it is manifest, to be laid 
down from the widest possible survey of facts ; 
but as, by the supposition, it has been formed 
from a very partial view, should any hostile facts 
subsequently present themselves, such facts, in- 
stead of being allowed to modify the general law, 
are too often brought under it by an adroit ex- 
tension or perversion of the terms in which the 
law is expressed. 

A curious instance of this verbal legerdemain 



172 THE THEOEY OF SEASONING. 

was furnished by some political economists many 
years ago, in order to support the sweeping gene- 
ralisation, that the values of all commodities are in 
direct proportion to the quantities of labour be- 
stowed upon them. A number of instances were 
pointed out in which this did not hold; and, 
amongst the rest, the instance of wine, which, by 
being simply kept in a cellar without any fresh 
expenditure of labour upon it, becomes greatly en- 
hanced in value. Such cases evidently required some 
modification of the general principle (or rather an 
ascent to a higher principle, embracing both kinds 
of instances) ; but the economists in question 
were not to be driven from their position by 
such hostile facts as these. They preserved the 
integrity of their rule by maintaining that, when 
wine had been raised in value (suppose one tenth), 
by being kept a considerable period, one tenth of 
additional labour might be correctly considered as 
expended upon it, on the ground that capital 
might be said to be employed during that time, 
and capital is hoarded labour. Thus an incorrect 
generalisation of facts was supported by an equally 
incorrect generalisation of a word. 

The greatest source, however, of erroneous con- 
clusions, transcending all others in an almost im- 
measurable degree, is the gratuitous assumption of 
false premises without any evidence at all. These 
erroneous premises are assumed in various ways. 



ERRONEOUS CONCLUSIONS. 173 

A large majority of them are mere prejudices fas- 
tened upon the mind by tradition, or instilled into 
it by dogmatic instruction, or caught from the 
unanimous voice of society or of books, and are 
never suspected of error. 

They thus come to form the laws from which, 
on a thousand occasions, we unhesitatingly reason, 
and are the foundation of those extraordinary 
erroneous conclusions which have been prevalent 
amongst mankind in every age and every country. 

But what are prejudices now must have been at 
the outset direct errors ; and it is a part of the 
inquiry, how they came first into being; what 
were the original causes of the fallacies which have 
thus hardened into prejudices, and been transmitted 
from one age to another. 

The chief of these causes we shall find in cir- 
cumstances which still prevail, and perpetually 
form new and direct sources of error, such as im- 
perfectly observing the objects and events around 
and within us, and thence drawing erroneous 
general inferences as already explained, mistaking 
unconscious inferences for facts, and, above all, 
supposing facts without any evidence, misappre- 
hending for realities what are mere hypothetical 
assumptions of our own minds, mere figments of 
imagination ; to which causes may be added as 
frequent in every age, particularly amongst the 
rude and uncultivated, a strong tendency to exag- 



174 THE THEORY OF REASONING. 

geration, and to the invention as well as to the 
belief of marvellous events. 

In all these, and numberless other ways, man- 
kind come to have in their minds wrong grounds of 
inference, false facts, and erroneous general propo- 
sitions, from which they reason ; or, to express it 
still differently, unsound premises, from which 
they deduce conclusions of corresponding unsound- 
ness. 

In reference to all these sources of erroneous con- 
clusions, there is one point on which it is almost 
impossible to insist too strongly — the extreme im- 
portance of rigorously scrutinising facts, and terms, 
and inferences, at the commencement of all inves- 
tigations. 

The origin of a false theory, or a series of false 
doctrines, may be generally detected in some error 
lurking in the very first propositions from which it 
sets out ; and it scarcely needs enforcing on the 
inquirer, of how much more consequence an error 
is there than at any subsequent stage of the 
treatise or speculation in which it occurs. 

It is like an oversight committed in the second 
or third term of a geometrical progression, com- 
pared to one of equal numerical magnitude in the 
last term of a long series.* 



Example : 2. 4. 8. 16. 32. 64. 126., error of 2 in the 7th term. 

2. 4. 6. 12. 24. 48. 96., error of 2 in the 3d term, 

increased to 32 in the 7th. 



ERRONEOUS CONCLUSIONS. 175 

The justness of such general observations as 
have been now given is never so well discerned as 
when they are elucidated by particular instances ; 
and I will, therefore, briefly cite examples of the 
three principal sources of erroneous conclusions 
described, viz., ambiguities of language, insuffi- 
cient or faulty induction, leading to undue gene- 
ralisation, and the assumption of mere suppositions 
for real facts. 

The examples which I shall adduce of these 
three several errors, I have selected with the view 
of also showing how needful it is to examine, with 
the utmost vigilance, whether such errors infect 
the original positions from which any theory sets 
out. 

Of the first-named error a memorable illustration 
is to be found in the writings of Mr. Bicardo. A 
number of erroneous and nugatory conclusions 
in his principal work on Political Economy, of 
which some appear glaringly paradoxical, and 
others, on a cursory inspection, wear such a sem- 
blance of profundity, as to have misled distin- 
guished economists, had their source in a con- 
fused and ambiguous use of the word value, which 
may be detected even in the first section of his 
first chapter, and pervades the whole of his 
treatise. 

The readiest way of explaining and elucidating 
this ambiguity will be to cite a passage from a 
work in which it is freely exposed. 



176 THE THEOEY OF REASONING. 

" While Mr. Eicardo professedly used the term 
value in one sense only [that of purchasing power], 
he insensibly lapsed into a different sense." " The 
passage in his book where this transition is 
made, the turning point, if I may so call it, is in 
the very first section. Having quoted a few sen- 
tences from Adam Smith, which explain that, in 
rude ages, the quantities in which commodities 
were exchanged would be determined by the quan- 
tities of labour necessary to acquire them, he pro- 
ceeds : 4 If the quantity of labour realised in com- 
modities regulate their exchangeable value, every 
increase of the quantity of labour must augment 
the value of that commodity on which it is ex- 
ercised, as every diminution must lower it.' Now 
here Mr. Eicardo begins with using value in the 
sense of exchangeable value, or purchasing power; 
and, as he uses it in that sense in the premises, 
he is bound to do it in the conclusion ; and the 
conclusion is true enough, if he means that every 
increase in the quantity of labour must augment 
the value of that commodity on which it is exer- 
cised in relation to other commodities which con- 
tinued to require only the same labour as before. 
This, however, although perfectly consonant with 
his doctrines, will not be found to have been Mr. 
Eicardo' s peculiar meaning. In this proposition 
he did not extend his view beyond the one commo- 
dity. The word value did not carry him over, as 
the phrase power of purchasing would have done, to 



ERRONEOUS CONCLUSIONS. 177 

the consideration of some other. An attentive 
reader will perceive his meaning to have been, 
that every increase of labour would augment the 
value of the commodity on which it was exercised 
without reference to any other commodity. This 
proposition is the hook from which all his other 
propositions inconsistent with his own definition 
depend. This one false step made, he very lo- 
gically falls into the obscurities and paradoxes 
which have excited the admiration of his disciples, 
and the astonishment of every body else."* 

The theory of Mr. Malthus on population is a 
most instructive example of the second error. It 
shows what a long train of unsound inferences may 
be consequent on the precipitate formation of a 
general law from an insufficient collection of facts ; 
and this is to be found at the outset of his specula- 
tions, where it is assumed, on the slenderest grounds, 
that in all the various races of men, under all cir- 
cumstances, habits, climates, and conditions, there 
is a uniform tendency to double their numbers in 
twenty-five years or less ; a rate of increase which 
becomes certain provided they are supplied with 
sufficient food, shelter, and clothing; but such a 
sufficiency, in the long run, they never can be sup- 
plied with, inasmuch as food increases in only an 
arithmetical ratio. Even if Mr. Malthus's theory 

* Letter to a Political Economist on the Subject of Value. 
See also "A Critical Dissertation on the Nature, Measures, 
and Causes of Value, 1825," by the Author. 

N 



178 THE THEORY OF REASONING. 

could be proved to be correct, the way in which he 
obtained his fundamental principles would ever re- 
main a memorable instance of hasty generalisation, 
not merely as represented by others, but as recorded 
by himself. 

It fortunately happens that we have an account 
of the matter in his own words. Nothing can be 
more explicit than the following statement. 

" It has been said," writes Mr. Malthus, " that I 
have written a quarto volume to prove that popu- 
lation increases in a geometrical ratio, and food in 
an arithmetical ratio ; but this is not quite true. 
The first of these propositions I considered as proved 
the moment the American increase was related, and 
the second proposition as soon as it was enunciated. 
The chief object of my work was to inquire what 
effects these laws, which I consider as established 
in the first six pages, had produced and were likely 
to produce on society." * 

Thus of two important propositions, teeming 
with consequences, he considered the first (which 
in truth required to be substantiated by extensive 
research and cautious discrimination) as proved by 
one solitary instance; and the second (scarcely to 
be established by a less severe process) as purely 
self-evident. This is assuredly not the way in 
which the foundation of weighty and comprehensive 
theories ought to be laid.f 

* Essay on Population, vol. ii. p. 453., 6th ed. 

t The reader who may wish to reconsider this important 



EKRONEOUS CONCLUSIONS. 179 

Of the third error in our list we have a striking 
instance, almost equally instructive in its logical 
results although less momentous in its practical 
consequences, in the great fallacy which forms the 
basis of Berkeley's celebrated Theory of Vision. A 
more decided case of the assumption of purely 
imaginative facts as real and incontrovertible pre- 
mises can scarcely be adduced from the records of 
philosophical speculation. The false step in question 
is committed in the second paragraph of his Essay, 
in which, with a perfect unconsciousness of what he 
is doing, he converts distance (an abstract term) 
into a material line, and represents it as both the 
patient and the agent of physical operations, which 
are of course wholly fictitious.* 

As this passage, however, will form the subject of 
particular comment in an Appendix to the present 
treatise, it is needless, after quoting it below, to do 
more here than point out the general character of 



question is recommended to consult Mr. Doubleday's " True 
Law of Population," and an able tract by Mr. Hickson, first 
published in the Westminster Review, entitled, " An Essay on 
the Principle of Population," containing, in my opinion, the 
justest view of the subject yet given to the world, and re- 
markable for its abstinence from hasty generalisation, the 
besetting sin of Mr. Malthus. 

* "It is, I think, agreed by all that distance of itself and 
immediately cannot be seen. For distance being a line directed 
endwise to the eye, it projects only one point in the fund of 
the eye. Which point remains invariably the same whether 
the distance be longer or shorter." 

N 2 



180 THE THEORY OF REASONING. 

the fallacy which it contains and its position in the 
very van of his logical forces. 

Such instances as these strikingly show the ne- 
cessity of scrutinising the doctrines of even the 
most eminent philosophers in their very origin, as 
well as exemplify the prevalence and importance of 
those errors which lurk in ambiguities of language, 
unwarranted generalisations, and assumptions of 
fiction for fact. 

Whoever attentively reflects on these examples, 
and on the suggestions regarding them, which have 
been offered in the present chapter, will probably 
agree with the author that, although the first two 
causes of fallacy extensively prevail, yet the greatest 
revolution remaining to be produced in human 
thought will arise from a diminution of the last- 
mentioned source of erroneous conclusions, or, in 
other words, from an examination of propositions 
expressive of facts assumed without any evidence. 

The progress of physical science may be looked 
upon now as secure. In this department of know- 
ledge, the human mind has succeeded in placing 
itself on the right track ; and although some im- 
provement may be effected in the exact expression 
of abstruse scientific principles, what chiefly remains 
to be done, is to go forward from the points already 
attained, to the investigation of facts hitherto 
overlooked, or not yet brought to light, or not suf- 
ficiently examined, with all the aid supplied by 
the exquisite instruments and subtle methods of 



ERRONEOUS CONCLUSIONS. 181 

calculation invented by modern ingenuity. The 
proper mode of proceeding is here insured by such 
illustrious examples of successful investigation, 
that the necessity of rules and formulas is almost 
superseded. But in morals, metaphysics, theology, 
and politics, with all subjects belonging to social 
science not comprehended by those terms, and I 
may add in the science of medicine, a different 
aspect of affairs presents itself. Here there are 
innumerable gratuitous and baseless assumptions, 
received with entire faith as unquestionable and 
almost self-evident first principles, of the ground- 
lessness of which no suspicion is entertained. 

These are often mixed with truths, and the 
various deductions from both being perpetually 
intermingled with the original data and with each 
other, the result is a chaos of opinions, from which, 
in moments of speculative despondency, it seems, 
to the philosophic mind, impossible for the human 
race to be extricated. 

The only method of extrication is for the in- 
quirer to allow no facts, no propositions, no doc- 
trines, no principles, or whatever else they may be 
called, to pass before him on any question which 
he has undertaken to examine, without scrutinising 
their character and carefully investigating the evi- 
dence on which they rest, or are supposed to rest ; 
and where there is no evidence at all, attempting 
to trace the groundless assumptions to their origin 

* 3 



182 THE THEORY OF REASONING. 

in mal- observation, misapprehension, ignorance, 
falsehood, the love of fiction, or other causes. 

This course is doubtless opposed by a general 
and a reprehensible repugnance to review esta- 
blished doctrines, and by the mischievous prejudice, 
which has so long obstructed philosophical inquiry, 
that opinions are legitimate objects of moral appro- 
bation and censure; that for the conclusions to 
which a man is brought in the free exercise of his 
intellect, he may be justly subjected to moral 
condemnation. 

The destruction of this senseless and pernicious 
dogma, which subjects the thinking few to the 
despotism of the unthinking many, would sweep 
away one of the greatest impediments, not only to 
the progress of truth, not only to the advance of 
sound morality, but to the reciprocation of kind 
feelings and good deeds, to the peace of the in- 
dividual, the family circle, and the community ; 
in a word, to the happiness which is ready to flow 
upon the human race from a thousand sources 
were it permitted to do so. 

It is not yet adequately perceived how much 
the predominance of speculative error costs the 
world. 



APPENDIX. 



N 4 



APPENDIX, 



ARTICLE I. 

AN ANALYSIS OF SOME TRAINS OF REASONING. 

To elucidate and at the same time to test the accuracy 
of those views of the reasoning process which have been 
unfolded in the preceding chapters, perhaps the most 
effectual way will be to examine some specimens of argu- 
mentation, not fashioned for the purpose, but taken from 
productions written without reference to theories or canons 
of logic. The usual course in logical treatises is to frame 
syllogisms or enthymemes specially adapted to exemplify 
the rules and observations brought forward ; and this has 
its advantages ; but it ought not to supersede an exami- 
nation and analysis of the actual reasoning employed by 
men in their ordinary discourse and writings to convince 
each other. The latter procedure may be expected to 
bring out some points which would have otherwise escaped 
remark, and, at all events, it is likely enough to put to the 
test the soundness of any theory on the subject. 

Section 1. 

Analysis of a Demonstration in Euclid. 

The first instance of reasoning which I shall select for 
this purpose, is the demonstration of a theorem in Euclid. 




186 APPENDIX. 

Theorem. 
An exterior angle of a triangle is equal to both its 
opposite interior angles, and all the interior angles of a 
triangle are together equal to two right angles. 

The exterior angle 
BCD formed by the 
production of the side 
ac of the triangle 
ABC, is equal to the 
two opposite interior 

\/ angles cab and cba, 

and all the interior 
angles cab, cba, and bca, are together equal to two 
right angles. 

Through the point C draw the straight line ce parallel 
to ab. 

1. The interior angle bac is equal to the exterior angle 
ecd, because ad is a straight line falling upon the 
parallel lines AB and CE. (book i. prop. 29.*) 

2. Again, the alternate angles ABC and BCE are equal, 
because BC is a straight line falling upon the parallel 
lines AB and CE. (i. 29.) 

3. Wherefore the two interior angles BAC and ABC are 
together equal to the two angles ECD and bce or the 
whole angle BCD. 

4. When to each of these equals is added the angle bca, 
the angles bca, bag, and abc, which are the three 
interior angles of the triangle, are together equal to 
the angles BCA and BCD. 

5. But the angles bca and BCD being made by the 
straight line bc on the same side of the straight line 
ad, are together equal to two right angles, (i. 13.) 

6. Wherefore the three interior angles of the triangle are 
also together equal to two right angles. 

* Simson's Euclid. 



APPENDIX. 187 

In this demonstration there are six distinct steps of 
reasoning. The first and second steps, although in ap- 
pearance enthymemes, are in reality syllogisms, having 
the major premises not indeed formally stated nor yet 
suppressed, but only referred to as propositions formerly 
proved, viz., "a straight line falling upon two parallel 
straight lines makes the exterior angle equal to the interior 
opposite one," and " a straight line falling upon two parallel 
straight lines makes the alternate angles equal." 

The general principle or maxim exemplified by these two 
arguments, is the dictum de omni et nullo. In the latter 
argument, for example, the equality of the alternate angles 
ABC and bce is not self-evident, but proved by the alle- 
gation previously demonstrated that all such angles are 
equal. 

The third step is an argument not requiring a major 
premise. The angles bac and ABC having been shown 
to be respectively equal to ecd and bce, the first pair 
together are intuitively discerned to be equal to the second 
pair together, or to BCD. 

To such reasoning, indeed, a major premise is, as we all 
know, sometimes appended, by citing the maxim (forming 
the 2nd Axiom in Simpson's Euclid) " if equals are added 
to equals the wholes are equal," but, as already explained, 
this can bring no confirmation to the argument, which is in 
itself perfectly conclusive. The axiom cited is only the 
general principle exemplified by the reasoning, and when 
introduced as a major premise is a logical impertinence. 

The fourth step is also a self-evident argument requiring 
no major premise, and exemplifies the same axiom, " when 
equals are added to equals the wholes are equal," or more 
correctly, " when the same quantity is added to equals, the 
wholes are equal." 

The fifth step is again an apparent enthymeme, with the 
major premise not formally stated but indicated as having 
been previously proved, viz. " the angles which one straight 



188 APPENDIX. 

line makes with another on the same side of it are equal to 
two right angles." The general principle exemplified is 
here, as in the first and second steps, the dictum de omni et 
nullo. 

The sixth step, like the third and fourth steps, is a self- 
evident argument, not properly admitting or requiring any 
major premise, being complete as an enthymeme; but it ex- 
emplifies a different axiom, viz. " things which are equal to 
each other are equal to the same thing ; " which is the con- 
verse of Euclid's, " things which are equal to the same are 
equal to each other." 

In this demonstration, then, consisting of six steps of 
reasoning, three of the arguments require respectively a 
major premise, and three do not: the three former exemplify 
the dictum de omni et nullo, and the three latter exemplify 
respectively a mathematical axiom. 



Section 2. 

Analysis of a Passage in Burhe^s Letter on the French 
Revolution, 

The next specimen of argumentative composition which 
I purpose to examine, is a passage from Burke, requesting 
the reader to bear in mind that it is not my design to 
discuss the validity of the reasoning (although I may 
hazard incidental remarks on that point), but to exhibit the 
nature of the various arguments adduced. 

It may be useful to observe, before quoting the passage, 
that there is one very marked distinction between mathe- 
matical and what is usually called moral reasoning, or 
rather argumentative composition on moral and political 
topics. In the former, no proposition which is not self- 
evident is introduced without being proved. The latter, 
on the contrary, often abounds with mere assertions as well 
as arguments, presenting the two so intermingled that it 



APPENDIX. 189 

is not always easy to separate them. The reasoning, 
moreover, is not seldom elliptical, disjointed, and irre- 
gular, so that both skill and patience are required to 
reduce it into a definite shape and proper order. The 
portion of argumentative composition which I have now to 
analyse, is as follows : — 

1. "All persons possessing any portion of power ought to 
be strongly and awfully impressed with an idea that 
they act in trust ; and that they are to account for 
their conduct in that trust to the one great master, 
author, and founder of society. 

This principle ought even to be more strongly im- 
pressed upon the minds of those who compose the 
collective sovereignty than upon those of single princes. 

2. Without instruments, these princes can do nothing. 
Whoever uses instruments, in finding helps finds also 
impediments. Their power is, therefore, by no means 
complete. 

3. Nor are they safe in extreme abuse. Such persons, 
however elevated by flattery, arrogance, and self-opi- 
nion, must be sensible that whether covered or not by 
positive law, in some way or other they are account- 
able even here for the abuse of their trust. If they 
are not cut off by a rebellion of their people, they 
may be strangled by the very janissaries kept for 
their security against all other rebellion. Thus we 
have seen the King of France sold by his soldiers for 
an increase of pay. 

4. But where popular authority is absolute and un- 
restrained, the people have an infinitely greater, 
because a far better-founded, confidence in their own 
power. They are themselves, in a great measure, 
their own instruments. They are nearer to their 
objects. 

5. Besides, they are less under responsibility to one of 
the greatest controlling powers on earth, the sense of 
fame and estimation. 



190 APPENDIX. 

The share of infamy that is likely to fall to the lot of 
each individual in public acts, is small indeed; 

6. The operation of opinion being in the inverse ratio to 
the number of those who abuse power. 

7. Their own approbation of their own acts has to them 
the appearance of a public judgment in their favour. 
A perfect democracy is therefore the most shameless 
thing in the world. 

8. As it is the most shameless, it is also the most fear- 
less. No man apprehends in his person he can be made 
subject to punishment. 

9. and 10. Certainly the people at large never ought; 
for as all punishments are for example towards the con- 
servation of the people at large, the people at large can 
never become the subject of punishment by any human 
hand. 

11. It is, therefore, of infinite importance that they should 
not be suffered to imagine that their will, any more 
than that of kings, is the standard of right and wrong. 

12. They ought to be persuaded that they are full as 
little entitled, and far less qualified, with safety to 
themselves, to use any arbitrary power whatsoever ; 
that therefore they are not under a false show of 
liberty, but, in truth, to exercise an unnatural in- 
verted domination, tyrannically to exact, from those 
who officiate in the state, not an entire devotion to 
their interest, which is their right, but an abject sub- 
mission to their occasional will ; extinguishing thereby, 
in all those who serve them, all moral principle, all 
sense of dignity, all use of judgment, and all con- 
sistency of character, whilst by the very same process 
they give themselves up a proper, a suitable, but a 
most contemptible prey to the servile ambition of 
popular sycophants or courtly flatterers." 

Every one will see that this passage is a most complicated 
piece of reasoning. 



APPENDIX. 191 

As is frequently the case, the whole forms one main 
argument, and is meant to enforce one main conclusion, 
while, at the same time, it contains within it a number of 
subordinate arguments of various kinds, rather loosely put 
together and irregularly expressed. 

The conclusion which the writer endeavours to establish, 
stated as briefly as possible, is, that the people in a demo- 
cracy stand more in need than princes do of the check on 
their conduct supplied by a deep impression of the principle 
that they are responsible to God for the exercise of their 
power. And the sum of the reasons which he assigns for 
it is, that they have more complete power with fewer 
social and political checks upon it than princes have. 

The conclusion or proposition to be proved is stated in 
paragraph No. 1., and the rest of the passage is occupied 
chiefly with showing the checks from which popular 
authority is free. 

This main argument is obviously one of those enthy- 
memes which can derive no strength or confirmation from 
a major premise. In a very abridged form the reason- 
ing is,— 

The people in a democracy are under fewer social 

checks than princes are ; 
Therefore they stand more in need of the check of 
conscious responsibility to God. 

It would be puerile here to obtrude as a major premise 
the general proposition, " all who are under fewer checks 
than princes are (or than other persons are) stand more in 
need of the check of conscious responsibility to God." This 
is not a true major premise giving cogency to the conclusion, 
but it is the general principle or maxim which the argument 
exemplifies, or which may be educed from it, resembling in 
this respect the axiom " things equal to the same thing are 
equal to each other." 

In the next argument, marked No. 2., and subordinate 
to the main one, there is a distinct enunciation of a major 



182 APPENDIX. 

premise, and there is also an expressed minor immediately 
preceding it. Varying a little the language but not the 
meaning of this minor, and placing them in the usual order, 
we have the following syllogism : — 

Whoever uses instruments in finding helps finds also 
impediments ; 

Princes necessarily use instruments ; 

Therefore their power is by no means complete. 
But in drawing this conclusion from his premises our 
author uses an ellipsis in his reasoning. The only logical 
inference he could directly draw from them is, " therefore 
princes find impediments." In order to make the reasoning 
bring out the actual conclusion, recourse must be had to 
another argument, which, stated syllogistically, would be: — 

Whoever finds impediments has incomplete power ; 

Princes find impediments ; 

Therefore they have incomplete power. 
This syllogism is, nevertheless, of that kind in which 
the major premise is superfluous, or in other words imparts 
no force to the argument, but is merely a generalisation of 
it. Let us try this by reducing it to an enthymeme : — 

Princes in using instruments find impediments ; 

Therefore their power is incomplete. 
The force of the reasoning here lies in the implication 
of one thing by another, as in the case of a mathematical 
enthymeme. The argument is, in truth, an example of 
those inferences, already explained in the third chapter, 
where the same fact is presented to the mind in two different 
aspects, and it is argued that because it is true in the one it is 
true in the other. 

The argument numbered 3. has for its conclusion a 
clause tacked to the conclusion of the preceding argument, 
viz., "nor are they [princes] safe in extreme abuse," the 
connection in the train of thought appearing to be this : 
The power of princes is limited not only by the neces- 
sity of employing other men as instruments, but by and 



APPENDIX. 193 

danger of an extreme abuse of it. To prove his con- 
clusion as to the danger, he alleges that if they abuse their 
trust, they are subject either to be cut off by a rebellion of 
their people or to be strangled by their own janissaries. 
Thus, briefly stated, we have the following enthymeme : — 
Princes who abuse their power are liable to be cut off 

by rebellion or assassination ; 
Therefore they are not safe in the abuse of it. 
Here nothing would be gained by thrusting in the 
general principle, " no person who is liable to be cut off by 
rebellion or assassination is safe." It is one of those en- 
thymemes already described in the foregoing treatise, where 
the inference amounts to little more than a variety in the 
expression of the fact stated in the premise. 

Our author, having thus shown that there are certain 
limitations to the power of princes, proceeds to intimate 
that absolute popular authority is exempt from such 
limitations, although his language is not altogether precise 
or direct to the point. Instead of having, like princes, to 
employ instruments, the people, he says, are in a great 
measure their own instruments, and they have an infi- 
nitely greater confidence in their own power than princes 
have, because they have a far better founded confidence. 

This last clause, which in the extract is numbered 4, 
may be construed as a simple assertion that their greater 
confidence in their own power is caused by their confidence 
being better founded, the truth of which as a fact may be 
disputed. If it is regarded as an argument, we have the 
following enthymeme : — 

Where popular authority is absolute and unrestrained, 

the people have a far better founded confidence in 

their own power than princes have ; 

Therefore they have an infinitely greater confidence. 

This is a conclusion, however, not implied in the premise 

here stated. It may be naturally asked, is a better founded 

confidence entertained by mankind always a greater con- 

O 



1 94 APPENDIX. 

fidence ? and this being a matter of experience, to be as- 
certained by examining a number of instances, the argu- 
ment requires a major premise expressing or embodying 
that experience, as thus : — 

Whoever has a far better founded confidence in his 

own power than another person possesses, has an 

infinitely greater confidence. 
The argument is now completed : if you do not admit 
it, your objection would lie against the major premise as 
not true, and not against the reasoning as inconclusive. 
In point of fact, the major premise is not defensible ; it is a 
false law deduced from a partial and imperfect induction of 
instances, the most undoubting confidence being frequently 
entertained where there is the smallest foundation for it. 
It is scarcely needful to add that the argument, with the 
major premise as above given, exemplifies the dictum de 
omni et nxdlo. At the same time, it must be observed that 
the whole is an instance of contingent under the form of 
demonstrative reasoning. 

The next argument to be examined is numbered 5, in which 
the proposition maintained is that the people in a democracy 
are more exempt than princes are from another check — 
" they are less under responsibility to one of the greatest con- 
trolling powers on earth, the sense of fame and estimation ; " 
for which he assigns as a reason (although he does not in-r 
dicate it by a causal conjunction) that " the share of in- 
famy that is likely to fall to the lot of each individual in 
public acts is small indeed." 

Here again the conclusion is implied in the premise, and 
if a major proposition were introduced, it would be merely 
a generalisation of the argument. 

Argument No. 6. is to prove the proposition which forms 
the reason in the foregoing one : 

The operation of opinion being in the inverse ratio to 

the number of those who abuse power, 
The share of infamy likely to fall on each individual 

is small. 



APPENDIX. 195 

The reasoning here is elliptical but it is demonstrative. 
There is a change of terms also to be noted, which renders 
the whole less clear than it would be if a uniformity of 
language were observed, as in the following version 
of it: — 

The share of infamy falling on each individual is in 
the inverse ratio of the number of those who abuse 
power ; 
Therefore the share of infamy falling on each indi- 
vidual in a democracy (which consists of a large 
number) is small. 
The only premise in this argument is of the nature of a 
major premise, being a general proposition gathered from 
observation, and the conclusion is a particular instance 
coming under it. The principle exemplified is the dictum 
de omni et nullo. As the reasoning is a little complex, a 
minor premise might be introduced without puerility, and 
the logical dependence of the whole rendered clearer 
to common apprehension by a little amplification. 

The share of infamy falling on each individual is in the 

inverse ratio of the number of those who abuse 

power ; L e. if the number is large the share is small, 

if the number is small the share is large ; 

The number of persons in a democracy who abuse 

power is large ; 
Therefore the share of infamy falling on each indivi- 
dual is small. 
The argument No. 7. is short : " A perfect democracy is 
the most shameless thing in the world, because their own 
approbation of their own acts has to them the appearance 
of a public judgment in their favour." 

It is scarcely needful to point out that here again, 
although the reasoning is somewhat elliptical, there is no 
need of a major premise. 

Argument No. 8. is of a precisely similar character : " A 
democracy is the most fearless thing in the world, because 

o 2 



196 APPENDIX. 

no man apprehends in his person he can be made subject 
to punishment." 

The next passage exhibits a complication of reasoning; it 
consists, in fact, of two arguments numbered 9 and 10, and 
denoted by the causal conjunctions " for " and " as." The 
conclusion maintained is, " the people at large never ought 
to become the subject of punishment," and the reason as- 
signed is, " because the people at large can never become 
the subject of punishment by any human hand;" which 
last proposition is in its turn supported by the reason 
because "all punishments are for example towards the 
conservation of the people at large." 

The first of these arguments, No. 9., is singular : " The 
people cannot be punished by any human hand; there- 
fore they never ought." No one probably will contend that 
it will be mended by generalising it for the sake of obtain- 
ing a major premise, " Whoever cannot be punished by any 
human hand, never ought." 

The second argument, No. 10., is, in brief, "All punish- 
ments are for example to the people at large ; therefore none 
can be inflicted on the people at large by any human hand." 

This is an instance of an enthymeme consisting of a ma- 
jor premise and conclusion. To bring it into regular form as 
a syllogism would require the language to be altered : — 
All punishments which can be inflicted are for ex- 
ample to the people at large ; 
No punishment of the people at large can be for ex- 
ample to themselves ; 
Therefore no punishment of the people at large can be 
inflicted. # 

The passage No. 11. argues that as the people at large 
cannot be punished, it is of infinite importance that they 
should not imagine their will to be the standard of right 
and wrong. 

Here again we have an enthymeme not to be strength- 
ened in force by the introduction of a general proposition. 



APPENDIX. 197 

The next argument, No. 12., is somewhat longer and less 
plain. It may be summed up as follows : — 

The people are not more entitled, and are less qualified, 

than kings to use any arbitrary power; 
Therefore they are not tyrannically to exact from 
those who officiate in the state an abject submis- 
sion to their will. 
This concluding argument of the extract is manifestly of 
the same character as the last. 

The examination of geometrical and moral reasoning, 
which we have now gone through, may appear tedious, but 
it will not be fruitless in confirming the principles of the pre- 
sent treatise. It shows that both mathematical demonstration 
and argumentative composition, such as mankind actually 
employ in appealing to the understandings of each other on 
moral and political subjects, abound with reasoning of a 
varied character, exemplifying divers general principles or 
maxims, and it especially proves that many of the arguments 
employed are at once non-syllogistic and demonstrative. 



ARTICLE II. 



SOME SUGGESTIONS FOR THE EXAMINATION OF ARGUMENTATIVE 
COMPOSITION. 

The preceding examination of the nature of arguments 
may be useful to the student of Logic, by furnishing an 
example of the way in which such an analysis may be ac- 
complished. It is confined, however, to exhibiting the 
species and varieties of reasoning, while the points of the 
greatest importance to him are the truth of the premises 
and the validity of the conclusion ; and it has occurred to 
me that a few hints indicating the mode of proceeding to 

o 3 



198 APPENDIX. 

investigate these points would form a proper sequel to 
what has already been done. They are not designed for 
adepts but for students in Logic. 

On the supposition, then, that the student has a piece of 
reasoning or portion of argumentative composition before 
him, the following suggestions might be found useful in 
dealing with the arguments seriatim. 

1. Find the exact conclusion sought to be established by 
the writer, and state it as briefly but as nearly as 
possible in his own language. 

2. If the conclusion is obscure or ambiguous, endeavour 
to find out what the author meant ; and if it is doubt- 
ful which of two or more propositions he intended to 
maintain, examine the argument, as suggested in the 
following rules, first on the assumption of one and then 
on that of the other or others. 

3. Next find the reason or reasons assigned, and state 
them as the writer has done and as nearly as possible 
in his own language, stripping them, however, of 
redundant expressions and irrelevant matter. 

4. Examine the nature of the argument. 

a. If it is direct contingent reasoning, consider well 
whether the facts alleged are sufficient to warrant 
the general law, or, as the case may be, the par- 
ticular inference : if not sufficient, it is needless to 
proceed further. 

b. If the reasoning is ostensibly demonstrative and in 
the form of enthymemes, it may be well, when you 
are doubtful whether it is class-reasoning or not, 
to make it syllogistic by supplying what is called 
the missing or suppressed premise, since even should 
the last turn out to be needless, you will at all events 
have all the possible propositions before you ; and 
although needless, it must be true if the enthy- 
meme is valid. When the argument has been thus 
brought into a definite form examine the validity of 



APPENDJX. 199 

the syllogism ; and if it is fallacious, in consequence 
of confusion or ambiguity in the language or other 
cause, mark the fallacy, and your task is ended. 

5. In both the above cases (a and b) since the premises 
are insufficient to prove the conclusion deduced from 
them, it will be well to consider whether a modified 
inference may not be drawn from the facts as stated. 
The facts do not bear out the asserted conclusion, but 
they may bear out something short of it : what con- 
clusion do they enable us to deduce?* 

6. Suppose, however, the inference to be valid, the next 
step, whether the argument belongs to direct contingent 
reasoning or to demonstrative reasoning, is to examine 
the truth of the premises, or, in other words, of the 
facts asserted in them. The conclusion is warranted 
by the premises ; but are the premises themselves to be 
relied upon ? 

7. In this investigation of the truth of the premises, 
you may possibly find that although the propositions, 
as stated by the author, are inadmissible, yet the 
substance of them is true, or at least susceptible of 
being put into a less objectionable shape. In such 
cases, as your object is not to take advantage of mere 
errors in form, but to come at the truth, whatever it 
may be, throw the argument into the most forcible 
shape in which it can be exhibited, and then re- 
examine the whole. 

8. If you satisfy yourself that the premises are erroneous, 
and can point out the circumstances which make them 
so, it will be useful to trace the source of the error in 
the mind of the writer. Nothing seems to give us a 
greater command of a subject than to be able not only 
to see the mistakes which have been made regarding 
it, but to ascend to their origin. 

* See Chap. XI. sect. 2. of the preceding Treatise, 
o 4 



200 APPENDIX. 

9. Recollect that, in many cases, although you can 
show an argument to be fallacious, the conclusion may 
still be true, and all that you have done is simply to 
have placed it in the position of being unproved. 

10. In order to guard against the obscurity, vagueness, 
confusion, and ambiguity incident to language, en- 
deavour to conceive when practicable the actual things 
represented by words ; and when the terms are com- 
plex, decompose their meaning into its constituent 
parts. 

11. When the definition of an important word on which 
any of the reasoning turns has been given, make it a 
practice, in all obscure or dubious passages of the com- 
position where it is employed, to substitute the defini- 
tion for the term. If the writer under examination 
has furnished no definition of such a term, form one 
for yourself and use it in the same manner. 

12. When abstract general terms are used in any propo- 
sition, translate the proposition into concrete language, 
and try how the argument in which the proposition is 
employed will be affected by the change. 



ARTICLE III. 

THE PRECEDING SUGGESTIONS IN PART EXEMPLIFIED BY AN EX- 
AMINATION of Berkeley's celebrated argument to prove 

THE IMPOSSIBILITY OF SEEING DISTANCE. 

For the purpose of exemplifying the principal rules here 
given, I will take Berkeley's celebrated argument to prove 
the impossibility of seeing distance. It is in his own words 
as follows : — 

" It is, I think, agreed by all that distance of itself and 
immediately cannot be seen. For distance being a line 



APPENDIX. 201 

directed endwise to the eye, it projects only one point in 
the fund of the eye. Which point remains invariably the 
same whether the distance be longer or shorter." 

According to our first rule, we have to begin the exami- 
nation of this argument by finding the conclusion which it 
seeks to establish. Berkeley has placed it on the very 
threshold of his treatise : — 

" Distance of itself and immediately cannot be seen." 

This conclusion or thesis appears to be clearly and unam- 
biguously expressed. I shall have in the sequel to object 
to the use here made of an abstract term ; but for the present 
let us take the proposition as it is given. 

We next proceed to comply with the third rule. 

The reason assigned for the conclusion is, that " distance 
projects only one point in the fund of the eye ; " and in 
proof of this latter proposition, a reason is also assigned, 
viz. that " distance is a line presented endwise to the eye.'' 

There are obviously here two separate arguments which 
are ostensibly of a demonstrative character, and which, in 
compliance with our fourth rule, we may spread out into 
two syllogisms, reversing the order in which the proposi- 
tions are presented by Berkeley. 

First Syllogism, 

Lines directed endwise to the eye project only one 

point in the fund of the eye ; 
Distance is such a line ; 
Therefore distance projects only one point in the fund 

of the eye. 

Second Syllogism. 

Whatever projects only one point in the fund of the 

eye cannot be seen ; 
Distance projects only one point there; 
Therefore distance cannot be seen. 



202 APPENDIX. 

Looking at these syllogisms agreeably to the latter part 
of our fourth rule, I find that they are perfectly correct. 
A scholastic logician cannot find in them any non-distribu- 
tion of middle terms or illicit processes ; the language is not 
ambiguous ; and every one of common discernment must see 
that they are conclusive. 

Nothing remains, then, but, in compliance with the sixth 
rule, to examine the truth of the premises. 

It will be obvious to all that the major premise of the 
first syllogism, if it has any meaning at all, must signify 
material or physical lines. If it meant any thing else it 
would be palpably inadmissible, since imaginary or hypo- 
thetical lines can project no points on the retina. The pro- 
jection of points, or more accurately the images of points, 
on the retina, is a physical operation ; and even in this sig- 
nification the predicate can be affirmed only of material 
lines stopping short of the eye. Of a material line directed 
endwise to the eye, the end would undoubtedly project a 
point on the retina, if it did not approach too near that 
organ ; but if it entered the eye it would project no point 
at all. 

The major premise, then, is true only if material lines are 
understood, and only if such lines stop short of the eye. 

Hence the minor premise, which asserts that distance is 
such a line as is spoken of in the major, cannot be admitted. 
If distance can be correctly termed a line at all, it can in 
no sense be termed a material line, and it would be absurd 
to speak of it as a line not reaching the organ of vision : 
but distance cannot, in fact, be termed a line at all with any 
correctness or even definite meaning, although it may be 
measured by a line. 

The minor premise being thus shown to be in every way 
inadmissible, the conclusion of the first syllogism is not es- 
tablished : distance is not proved to project even one point 
in the fund of the eye. 

The minor premise of the second syllogism, being the 



APPENDIX. 203 

same proposition as the unproved conclusion of the first, 
falls equally to the ground, and carries the whole syllogism 
along with it. 

But if this minor premise were admitted, the second syl- 
logism must share the fate of its predecessor. The major 
premise is not only untrue, but the very opposite of the 
truth ; for whatever projects a point, or, more accurately, 
the image of a point, upon the retina, must be seen ; and if 
distance projects such a point (which it cannot be said to 
do, as the assertion has no real meaning), distance must be 
seen. 

It has been supposed by some, that by lines directed 
endwise to the eye, Berkeley meant rays of light; but, if 
we try this supposition, we shall only be landed in fresh 
difficulties. What can be made of such a proposition as 
" distance is a ray of light directed endwise to the eye " ? 

Discarding, however, any rigid exaction of consistent 
language, let us, in the spirit of our seventh rule, en- 
deavour to put the argument in its best imaginable form : 

Bodies, at various distances, all send rays of light to the 
eye ; which rays must, of course, vary in length with the 
distances : now, as these rays are all right lines, presenting 
their ends to the retina, it is plain that the eye cannot see 
the different lengths of the rays, nor, consequently, the 
distances of the objects whence the rays proceed, any more 
than if a bundle of rods of various lengths were presented 
to it endwise, it could perceive that one rod was longer 
than another. 

Here we have two consecutive arguments. 1. Rays of 
light coming from objects present their ends to the eye ; 
therefore the lengths of the rays cannot be seen. 2. Inas- 
much as the lengths of the rays cannot be seen, the dis- 
tances of the objects whence they proceed cannot be seen. 

In reply to the first argument, it may be remarked, that 
it is a superfluous undertaking to prove that the lengths of 
the rays of light proceeding from objects to the eye cannot 



204 APPENDIX. 

be seen, since no part of such rays can be seen, neither the 
ends nor the lengths. They are so far from being seen, 
that it is only a small number of mankind who are aware 
that such things as rays of light, proceeding from the ob- 
jects in view, are concerned in the act of vision. That the 
lengths of such rays are not perceptible, is, therefore, a 
notorious fact. But the second argument goes on to allege 
that as the eye cannot see the various lengths of the rays, 
it cannot see that the objects from which the rays come 
are at various distances. Why not? What incompati- 
bility is there between rays being invisible and objects 
being seen to be at various distances from the spectator ? 
Here is, in fact, an assumption of the very thing to be 
proved. 

The bundle of rods furnishes no analogous case. Rods 
are visible objects, rays are invisible: rods, when pre- 
sented endwise to the eye, stop short of that organ ; rays 
enter it and fall on an internal membrane: the ends of 
rods are external objects which are seen by means of rays 
of light proceeding from them, while to say that the ends 
of rays are external objects seen by means of other rays 
proceeding from them would be self-evidently absurd. 

It is highly probable (to touch upon the inquiry suggested 
by Rule 8.) that this false analogy between bundles of rods 
or other material straight lines and rays of light, originally 
misled Berkeley, as it has undoubtedly misled some of his 
followers.* We see clearly how it may have been the 
source of his ingenious but unsubstantial paradox, and how 
it may have betrayed philosophers who ought to have known 



* " How can vision of itself give us any notion of the distance of 
bodies, when we know that the light reflected from them falls in 
straight lines on the eye, and can present only the ends of these lines 
to the organ? You can have no notion of the length of a line by 
being touched merely with one of its ends. We could as well know 
the length of a staff, by having our eyes confined merely to the breadth 
of its head." — Young's Lectures on Intellectual Philosophy, p. 113. So 
loosely is philosophy sometimes written. 



APPENDIX. 205 

better, into the mistake of regarding as a question in optics 
what is purely a metaphysical theory. 

In the preceding exposure of the unsoundness of 
Berkeley's premises, I have not adverted to one circum- 
stance which, when duly considered, is of itself sufficient 
to show their hollowness. 

The word distance is an abstract general term (such as 
forms the subject of Rule 12.), and no one has shown more 
forcibly than Berkeley himself that nothing can be repre- 
sented by such terms but what may be expressed in con- 
crete language; that there are no real abstract entities, 
either physical or mental, corresponding to them. 

For this reason, and not for the reason Berkeley assigns, 
it may be truly affirmed in one sense that distance cannot 
be seen. Distant objects may be seen to be distant, but an 
abstract quality corresponding to the term distance can be 
neither seen nor even conceived. 

His proposition, therefore, must be translated from the 
abstract into the concrete, when it will appear thus: 
" Objects at different distances from the spectator cannot 
of themselves and immediately be seen by him to be at 
different distances." 

This is Berkeley's real meaning; but when it is thus 
brought out in concrete language, the reasons he assigns 
for his conclusion no longer apply, as any one will find on 
trial. Who can bring to bear on the conclusion, as here 
translated, such propositions as, "distance is a line pre- 
sented endwise to the eye," and " distance projects only one 
point in the fund of the eye ? " 

It may be presumed that at the very early period of life 
when he wrote the " Essay on Vision " he had not attained 
to those clear views of the nature of abstract terms which 
he afterwards gave to the world in the Introduction to his 
" Treatise on the Principles of Human Knowledge ;" other- 
wise he would scarcely have fallen into the errors not only of 



206 APPENDIX. 

speaking of that which is denoted by an abstract term as a 
physical or material subject and agent, presenting ends to 
the eye and projecting points on the retina; but of making 
these imaginary operations the sole evidence of his main 
position. 

It is one of those instances (abounding in metaphysical 
speculations) in which ascribing a real separate existence 
and agency to what is represented by an abstract term has 
contributed to lead philosophers into very remarkable errors, 
and to perpetuate the influence of such errors over the 
human mind. 

It must be kept in recollection, agreeably to our ninth 
rule, that the preceding examination of Berkeley's argu- 
ment may possibly show only that his conclusion is un- 
proved, not that it is erroneous. In point of fact, such is 
the case. His alleged premises are shown to be false, but 
it is still possible that the proposition which he has at- 
tempted to prove by them may be true. The reader who 
is desirous of entering further into the question may 
consult two works by the present writer in which it is dis- 
cussed at considerable length.* 

After wading through the preceding directions and 
exemplifications, the young student may probably exclaim 
that the examination of all arguments in this way would 
require a vast deal of trouble. And there can be no doubt 
at all that to learn to think with accuracy and precision 
does require no small labour, but labour which cannot be 
evaded if the object is to be gained. He who wishes to 
obtain the power of correct reasoning must pay the price. 
There is, nevertheless, this consolation and cheering pros- 



* A Review of Berkeley's Theory of Vision, designed to show the 
unsoundness of that celebrated Speculation. 8vo. 

A Letter to a Philosopher, in reply to some recent attempts to 
vindicate Berkeley's Theory of Vision, and in further elucidation of 
its unsoundness. (Pamphlet.) 



APPENDIX. 207 

pect in view, that when by sedulous application the habit 
has once been acquired, the subsequent exercise of it will 
become comparatively easy, and will be agreeable even in 
those cases (unavoidably of frequent occurrence) in which 
it will still remain laborious. 



THE END. 



Works by the same Author, in Politics and Political 
Economy, 



A DISCUSSION OF PARLIAMENTARY REFORM, by 

a Yorkshire Freeholder. (Pamphlet.) 

THE RATIONALE OF POLITICAL REPRESENTA- 
TION. 8vo. 

THE RIGHT OF PRIMOGENITURE EXAMINED, by 
a Younger Brother. (Pamphlet.) 

A CRITICAL DISSERTATION ON THE NATURE, 
MEASURES, AND CAUSES OF VALUE, chiefly in 
reference to the Writings of Mr. Ricardo and his Followers. 
8vo. 

A LETTER TO A POLITICAL ECONOMIST, occasioned 
by an Article in the Westminster Review on the subject 
of Value. 

MONEY AND ITS VICISSITUDES IN VALUE AS 
THEY AFFECT NATIONAL INDUSTRY AND 
PECUNIARY CONTRACTS. 8vo. 

A DEFENCE OF JOINT-STOCK BANKS AND 
COUNTRY ISSUES. (Pamphlet) 

QUESTIONS IN POLITICS, POLITICAL ECONOMY, 

&c, for Discussion in Literary Societies. 



London: 

Spottiswoodes and Shaw., 

New-street-Square. 



W : 







%A* 



^, 






* o 






- ^ ^ 



\ ■ % 



^ A* * -« 

- 






\0 -V 






,x^ 







1 



v^-. 



■^ 






. v> <v - 




V 









• 



,-V 






Deacidified using the Bookkeeper process. 
Neutralizing agent: Magnesium Oxide 
Treatment Date: Sept. 2004 

PreservationTechnologies 

A WORLD LEADER IN PAPER PRESERVATION 

1 1 1 Thomson Park Drive 
Cranberry Township, PA 16066 
(724)779-2111 



^ 




c$> •'-, 






- %■ 







